I seem to recall inconsistencies with their use of oxygen as well, and I'm going to watch for that on my second viewing. I assume that whenever they're wearing full body armor and travelling in reverse, they have an oxygen supply under the helmet.

I feel the whole oxygen thing was just a gimmick to create tension and add an element of danger to traveling in reverse, and it wasn't really necessary other than that. Realistically they would also have to carry a LOT more oxygen. Granted they don't need compressed air as time reversed nitrogen would be just as inert as normal nitrogen, but that little bit of oxygen would not last long. Having had a friend on oxygen, who had to use the highest 5L/min setting, I can tell you even a good size portable tank wouldn't last long. For Tenet I think they would be using an even higher flow rate as it would not be supplemental. Then again, I sort of assumed he might be carrying a time reverser that was taking the air around him and reversing it. It really wasn't explained.

I am confused about the ending. I thought there was a trigger on the algorithm that was radio linked to the antagonist's heart beat, and that if he dies, the algorithm would be triggered, destroying the past? Very confusing. Must watch some explainers on that before rewatching the movie.