There is a distinct difference in a full game run depending on how you start it. If you select the first level rather than hitting the "New Game" button in the bottom left. You will keep all of the found equipment and be able to choose from it in all of the open combat mission. However, if you do choose to use the "New Game" button, any open combat missions will reset the items and even plate carriers that you previously found.

This absolutely changes the possible times that you can get. I.e. the highrise mission and being able to reach the roof in about 45 seconds with ascender (recieved once reaching the roof) vs about 2 minutes without.

it should at least be considered as a possibility though it's more likely that the new game+ category would be more popular.

There is a glitch during the mission that will prevent you from moving into the sniper field section. In order to prevent it you need to let the soldier, that was shot on the stairs of building 2, to start his line as you walk out of the Hassan video room. You can still walk through him once he starts speaking but if you don't let him then you can not progress later on in the mission.

Here is a video for examples of the glitch.