The issue of the forgotten ammunition pack in the first Taxi ride and the forgotten guns bag was due to budget cuts from Fox.
Fox forced the crew to cut $7 million from the script at the last minute from an already limited budget of a $58 million. In an interview with MTV Ryan Reynolds talks about the very low budget, “The budget isn’t what we hoped it would be, this [flanel shirt] is actually the suit,”
And Reynolds did have a hard time developing the movie due to the studios constraints, Reynolds said,
We went through such hell developing the script and which X-Men we
could keep and which we couldn’t and it just turned into a nightmare.
The studio would just say, ‘too expensive, too expensive, too
expensive’ to everyone. So finally we were like well, “What about
Negasonic Teenage Warhead” and they said, “Negasonic, what?”
And screenwriter Rhett Reese said ,
There was a reduction of action. We had a motorcycle chase between
Deadpool and Ajax (Francis) on the freeway that we took out. We had a
big, big gun fight in the third act that we took out and we basically
had Deadpool forget his guns as a means of getting around it. So there
were just reductions.
There is more on this on "How the Limitations of a Small Budget Forced the Deadpool Team to Make a Much Better Movie"