Purchased ME 3 a few days ago, after it's been on market for almost 2 years. Very disappointed and totally unexpected to find such a game breaking bug that hasn't been addressed. The bug is simply that picking up various types of weapon mods does not update your character (about half don't update, having done my priority to mars mission). Thus, you don't get one of core features of the game, using mods to upgrade your weapons.
Reading through the comments, it's apparent that it's caused by one of the patches. (1.05?). Those uninstalling / reinstalling appear to remove the bug, only until their system updates to the current version. The online version I bought from Origin for my PC is pre-patched, hence this is not an option. The only thing that works is using a third-party save game editor, which has me editing my character after missions, to decide whta to give him. It's rather immersion-breaking for me to be using a hack, viewing various plot / loot descriptors, and I'd guess about 75% of gamers would find it too difficult to follow the steps for this process, since you aren't simply clicking check boxes like in other editors.
