It's not just plot holes, but the entire way the story is written. Here are some of my thoughts:
The campaign begins with the BSAA picking up an amnesia-ridden drunk from a bar and sending him to war, after looking for him for six months as if the whole organisation could not afford any other captains to do the job. Looking at the dates of the bar encounter and the beginning of the playable part, you'll notice that there's only one day in between, which they probably needed to get to China, so they didn't even bother to let him train - Piers even comments on how he assumed Chris would be rather rusty. Well, honey, if you assumed that, maybe you should have been a little more considerate with this man who may look like your captain, but isn't really him at the moment.
So Chris, who still doesn't remember anything, then embarks on a journey that is determined by convenient coincidences: The hostages are free, the mission is technically over, but then Chris coincidentally gets his memory back and decides for his team to go after Ada/Carla. When they have her cornered, they coincidentally learn that there's an aircraft carrier preparing to launch dangerous virus missiles, so they set out to prevent that from happening. Just after achieving that as well, they coincidentally get a call from Leon who informs them that the personified key to saving the world and his partner have been kidnapped and need two knights in shining BSAA armour to come and free them.
I mean, really... Is it just me or were the developers pulling that out of their a$$es because they always had a few more chapters left to fill before the campaign could officially end? Compare this story to Leon's, for example: That one has a common thread running through the whole campaign, and whether you like said campaign or not, at least its narrative kind of makes sense from beginning to end.
Which leads to yet another thing that bothers me about Chris's part - the ending. Just look at that ridiculous character development: At the beginning Chris is severely pi$$ed off because, well, I've never had amnesia, but maybe that's what it does to you. Then he remembers he lost all his men and is even more pi$$ed off. Understandable. At the end he loses all his men again, yet he's suddenly happy and optimistic about it... wait, what? Did he try to smoke the BSAA badge Piers gave him as a farewell gift and get high from the C-virus-infected blood or something? And by the way, didn't we already have a very similar arc in RE5, which basically went from "I wonder if it's all worth fighting for" to "Yes, as long as Jill gets out of that ugly battlesuit eventually, it is"? Will every future game featuring Chris be like that from now on?
Then there's the flashback episode, which is my favourite from this campaign, but doesn't abide by flawless logic either. The obvious elephant in the room is that Chris does not know who Ada Wong is when Carla introduces herself as Ada, despite the Kennedy Report mentioned in RE5, and Ada pretending to be a BSAA agent in Damnation, which is set roughly a year before RE6 and probably didn't go completely unnoticed by the real BSAA. This was already discussed before and I argued that maybe Chris really didn't know Ada's name because Leon deliberately left it out of his report to protect his "girlfriend". But when I think about it, Ada tells her name (which is probably a fake identity, but that doesn't matter) to everyone she meets, and considering how often she gets mixed up in bioterror operations, I consider it highly unlikely that nobody on Chris's team, including the guys from HQ they're talking to via radio, has ever heard of her before.
Long story short: Chris's story is still decent for a videogame, but if I had handed a manuscript like that to my storytelling professor, he would have pummelled me with it.