Is 1 Corinthians 15:3-11 an Interpolation? No.
1 Corinthians 15:3-11 is an important passage because therein Paul provides the earliest written evidence of Jesus' resurrection. Notably, Paul recounts how he had "passed on" on this tradition that "he had received." The tradition explains that Jesus died, was buried, and appeared alive to Peter, the Twelve, John, the Apostles, the Five Hundred, and finally to Paul. Obviously, the tradition preexists Paul's own ministry and was given to him by other Christians. Moreover, Paul had the opportunity to discuss the tradition with at least some of the witnesses cited within it (Peter and James). Thus, the earliest tradition about the resurrection and appearances of Jesus pre-date those in the canonical gospels by decades and the tradition was espoused by someone who had the opportunity to discuss it with others who had experienced Jesus' resurrection. Pretty good historical evidence.
No doubt it is because of the value of the evidence that a few have questioned its authenticity, despite the manuscript traditions' unanimous attestation of its origins. Most who question this passage are hyper-skeptics on various internet forums whose pet theories do not fit with Paul's reliance on tradition and early attestation of the resurrection and appearances. In fact, only one "scholar" that I am aware of has come to this conclusion -- the fringe figure of Robert Price. Gathered here are the various objections I've seen raised to this passages' authenticity.
First, it is argued that the passage contains non-Pauline language. Of course, because the passage represents to be an inherited tradition this is hardly surprising. Whether preexisting tradition or interpolation the different linguistic characteristics would be explained.
Second, there are supposed incongruities between this passage and the canonical gospel's resurrection accounts. But these incongruities indicate authenticity, not interpolation. A Christian author familiar with the predominant Gospel stories is going to reflect them more than Paul, who wrote before the gospels were widely circulated.
Third, the passage refers to an appearance to "the 500" but the Gospels do not. But the 500 are not named and the emphasis is on many of them still being alive. (15:6). Some commentators have observed that the Gospels, written decades later, had less interest in recounting anonymous appearances -- especially when consulting those witnesses was much less practical (if possible at all). Other scholars have associated the appearance to the 500 with the ascension recorded in the first chapter of Acts or believe that it was the source of out which Acts' depiction of Pentecost developed. Others have placed it in Galilee. Whichever explanation is correct, if any, we cannot simply assume that the Gospel authors had no reason to leave it out -- especially given that they do not mention the appearance to James (perhaps they were connected with James or emphasized Jewish Christianity in some way). In any event, if any suspicion is cast on v. 15:6, the argument that all of vs. 3-11 must be interpolated as well goes far beyond the evidence. The evidence, if taken as such, only casts doubt on 1 Cor. 15:6. Nothing more.
Fourth, some have argued that because there is no Old Testament source for v. 3's reference to "three days according to the scripture", that the passage must be an interpolation. This argument proves too much. If there was no possible source in the OT for this reference for Paul, then there is no possible source for anyone -- even a later Christian interpolator. In any event, there was OT ammunition for Paul or a later Christian writer, such as Hosea 6:2, "After two days will he revive us: in the third day he will raise us up, and we shall live in his sight." Another possible reference is to the story of Jonah, of which the Gospel of Matthew makes explicit mention (1:17). (See also Gen. 42:18; Ex. 19:16; Josh. 2:22; Ezra 8:32; and Esther 5:1).
Fifth, some have argued that the inclusion of vs. 3-11 create an incongruity in the passage. This is a subjective argument with little to commend it. Reading the chapter with or without vs. 3-11 indicates that it makes more sense with the passage in than without it. So too with New Testaments scholars.
Finally, it has been argued that Paul's reliance on an established tradition in 1 Cor. 15:3-11 is incompatible with his statement in Galatians 1:12 that he did not receive his gospel from any man. This is Robert Price's argument, and he sees (or will suffer) no other explanation. But Price gives no regard to the different arguments being made. In Galatians, Paul is defending himself against Judaizers likely emphasizing their connection with the Jerusalem Church. He had to show his independence and the superiority of the message -- regardless of who preached it. (Gal 1:8). In Corinth, Paul faced a different problem. He was trying to convince a congregation that overly favored personal revelation to remember the traditions that had been passed on to them. He responded to them by stressing that what he had preached before was based on the common experience of all of the Apostles. (1 Cor. 15:8, 11).
And if we look closer, we realize that even in Galatians Paul admits that he learned about the gospel from other men. At the very least Paul was familiar with the faith while he was persecuting it. Paul stresses that his gospel is the "same" faith as he used to persecute. (1:22-23). He also emphasizes that he lived with Peter for more than two weeks and "submitted" his gospel to the Jerusalem leaders -- who approved it. Finally, as Dr. Thompson demonstrates, Paul's use of traditional, preexisting material is scattered throughout his letters -- thus belying any claim that he was adverse to such reliance. MB Thompson, 'Tradition,' in Dictionary of Paul and His Letters, page 944. In short, it appears that Price has exaggerated Paul's reluctance about relying on tradition in Galatians while ignoring or deemphasizing Paul's use of tradition elsewhere in his letters.
Now that we have seen that the case for interpolation is weak, we will explore additional reasons to accept the passages' authenticity.
First, as we discussed above, the manuscript tradition universally attests to the genuineness of this passage. It seems unlikely that all of the manuscript traditions would have accepted an interpolation that differed so substantially from the established texts and which appeared to contradict the gospels. In any event, the burden of proving an interpolation is certainly on the advocates. As noted above, that case fails to meet the burden.
Second, the patristic evidence gives no hint of any controversy over this passage. Rather, it shows that it was widely accepted and attested early. Around 110 AD, Ignatius quotes from 1 Cor. 15:8-9 in his Letter to the Romans (9:2). Thus, if verses 3-11 were interpolated it must have happened sometime between 54 AD and 110 CE. But even this window seems too wide because Paul continued to keep tabs on his churches until at least 62 AD and Ignatius assumed a position of leadership no later than the 70s. It appears, then, that the window is even smaller. Furthermore, Marcion's version of 1 Cor., circa. 130 AD, also has the passage. Not only is this attestation early, it is hostile. If Marcion had any reason to doubt a passage that so strongly affirms the humanity and death of Christ, as well as Paul's reliance on a tradition from Jewish Christians, he would have chopped it out as he did so many other Pauline verses.
Third, as admitted by Robert Price, the passage employs technical language used by Pharisees to denote the oral transmission of tradition. The use of technical Rabbinic language is much more likely to come from Paul's hand than a later, almost certainly Gentile, Christian interpolator.
Fourth, as discussed above, the variance between the Gospels and this passage point to authenticity. Later Christian scribes writing after the dissemination of the Gospels would likely attempt to conform the account to known tradition. Thus, the lack of a reference to an empty tomb, Paul's failure to mention the women's witness to Jesus' resurrection, the Gospels' failure to mention any appearance to James, and Paul's reference to the "Twelve" when the Gospels make it clear that Judas was dead, all indicate that the passage was written by Paul.
All told, the evidence is overwhelming that the passage is genuine. Indeed, there is simply no good reason to believe that its spurious. Arguments to the contrary are merely attempts to remove an unpleasant obstacle to some fringe theories.