The Post-Conciliar Sequence: The problem is that according to Gal. 2:1 Titus accompanies Paul to Jerusalem for the council, whereas according to Acts 16:1 Paul meets up with Timothy in Lystra some time after the council. First, the sequence is only a problem if Gal. 2:1-10 is to be equated with the trip of Acts 15. Since I'm inclined to identity Gal. 2:1-10 with the trip of Acts 11/12 (and Gal. 2:11ff. with the lead-up to the trip of Acts 15) it doesn't particularly bother me. Second, and Fellows's argument turns on this observation, Paul does not go immediately to Lystra after the council, but rather to Antioch, where he spends an unspecified amount of time. Thus, if we grant that Acts 15=Gal. 2:1-10 then we still potentially have time for Timothy/Titus to move on to the Lystra region ahead of Paul, and if we (as I am inclined to do) think that these meetings actually took place perhaps three or so years apart then there is no problem at all.
Paul's reference to both Titus and Timothy in the same letter: the supposed difficulty here is that Paul would not likely alternate between different names for the same person in the same letter. Just from my own writing and speaking habits I'm not sure if that holds. I will often alternate in a single discourse between names for the same person, especially nicknames. Fellows observes that this is likewise not unknown in ancient literature, and that moreover Paul will alternate between Peter and Cephas in Galatians, in fact in the span of a single sentence (cf. 2:7-9). As such this probably constitutes no objection at all.
The reference to Titus in 2 Timothy 4:10: this is, by my estimation, the only solid objection to Fellows's position. His argument is that 1) it's pseudo-Pauline, and 2) that the pseudo-Pauline writer is either a) referring to a different Titus or b) makes a mistake in distinguishing Timothy from Titus. #1 does indeed keep with the consensus view on the matter of authorship, so we'll grant #1 for the sake of argument. I'm not so sure about #2, however. Really, the only reason to suspect that the author of 2 Timothy has anyone other than the Titus otherwise known in the data or that the author is making a mistake by separating the two figures seems to be Fellows's own hypothesis. In other words, at what point is Fellows simply begging the question? What 4:10 tells us is that among the earliest known reception of the Pauline legacy Timothy and Titus were known to be separate persons (and this becomes all the more significant if one adopts the very minority position that Paul wrote 2 Timothy). Absent an otherwise compelling empirical case that the two figures must be the same person it seems to me that this very early witness to the non-identity of Timothy and Titus leaves Fellows's argument in somewhat tenuous condition.
As with many things in the study of the first Christian decades there is no knock-down argument in either direction. The problem is that, whilst tantalizing and perhaps solving certain problems, the Timothy=Titus hypothesis would seem to create a new, previously non-existent, problem, which frankly might be more difficult to resolve than the problems that the hypothesis aimed to resolve in the first place. As such, at this point, until I see something that would compel me to change my mind, I find myself placing it in the "Possible, but not probable," category.