Many have been having the same problem, myself included...
http://answers.ea.com/t5/Mass-Effect-3/weapon-mods-bug/m-p/354426#U354426
http://answers.ea.com/t5/Mass-Effect-3/Weapon-Benches-not-working/m-p/278146#U278146
http://answers.ea.com/t5/Mass-Effect-3/Unable-to-pick-up-campaign-weapon-mods/m-p/632314/highlight/f...
http://answers.ea.com/t5/Mass-Effect-3/Citadel-has-messed-up-Priority-Mars-and-maybe-others-too/m-p/698070#M8820
As of yet, Ive been doing extensive testing with frequent updates (shown in the last link). Along the way, I've had several members message me with their own solutions -- save before a mission, turn off system if you hapen upon the bug, relooad save, change difficulty to Insanity/ Normal or vice-versa; don't have an SMG equipped; don't equip any mods until you obtain all of them; never quick save; don't have auto-save on; etc -- and so far nothing has worked for me.
What I did -- and it has worked so far up to Rannoch -- is I deleted everything ME3 related on my system: saved files, dlc and patches, game progress, etc. Then I disabled my internet connection and booted up the game. This, however, means you must start a new game (transfer data from ME2 or start from scratch). You CANNOT transfer ME3 data. I tried it, and still found up I couldn't pick up certain weapon mods that weren't on Mars.
I also attempted to just delete dlc and patches, redownload DLC, and start up the game without being connected to the internet, but the bug still occurred in the same places, so I can only rule out that the bug is caused by BOTH DLC and patches. But simply deleting DLC and patches, and trying to utilize a ME3 save file, doesn't fix the problem either, as I've discovered. It seems that if you experienced the bug on a save file, no matter what you do, you will ALWAYS experience it on subsequent playthroughs.
So apart from those drastic measures I took mentioned earlier, I also disabled Auto-Save, disabled everything under the Online option (I know it doesn't matter since there is no connection, but I'm not taking chances here), I set the game to Insanity (this I'm pretty sure doesn't matter, you can very well set it to Narrative or Casual to get through the game much faster, sweeping up Weapon Mods like they were eggs on Easter!), and while playing I have not once changed my weapon load out, equipped a weapon mod, nor have I touched a weapons bench, all in fear of activating the bug. As I've said, so far I've managed to pick up every mod up to Rannoch. They register, as displayed by their appearance in the bottom right corner, and today I finally checked my weapons bench and did a checklist to see that I do indeed have everything up to this point (would've hated to discover I had nothing...).
After I beat the game, I'm going to download all 10 GBs of DLC to return my game to how it was, and transfer my data to see if all weapon mods are accounted for. If they are, I can finally set the game to how I like and enjoy it without worry of running into the troublesome bug. But until that happens, I'm going to keep playing this glitched-up-the-yin-yang game (how does a game this unpolished make it to the shelves is beyond me).
A few cautions if you attempt this workaround:
I PLAY ON THE PS3. The bug is on all platforms (maybe not the Wii...) so I'm not entirely sure my workaround is universal. My buddy has it on the PC, but he's assured me he hadn't run into the bug when he played last year; he hasn't played since. Lucky him!
SAVE OFTEN. There were many glitches before patching began, and there's nothing more irritating then getting so far and running into a hard freeze without having saved for hours on end. I'm used to Auto-Save kicking in, so I had to slowly step out of my comfort zone before I realized how important saving your game was.
TRY TO GET THROUGH THE GAME AS FAST AS POSSIBLE. It takes the fun out of the game when you give yourself limitations in your load-out, so try to do this playthrough with great haste. Tackle Missions and Quests that have Weapon Mods within them. Who cares about having enough War Assets by the end? You're just going to start a better playthrough when this one finishes. Attempting all of the quests will just absorb more precious time you could be spending on your ACTUAL playthrough.
And Finally...
UNDERSTAND THIS IS NOT A FIX TO THE ACTUAL BUG. This is a workaround. If this were an actual fix, you can keep all your game data and simply pick up mods without a problem. But this problem has been around for almost a year now. Bioware has yet to acknowledge it, and I doubt they'll be coming out with another patch. As far as I can tell, they're done with both DLC and patches for this game I(sad, really, as I was hoping for more Alternate Appearance Packs). I was just sick and tired of being ignored and not being able to enjoy my game to its full experience, so I sought out to do something about it.
So, there you have it. My remedy to the problem. I truly hope it helps, as I understand how frustrating this bug can be. I'll be sure to continue my updates (maybe in this post, since "Citadel has messed up Priority: Mars" is a very ambiguous title...), and let you know if I do in fact run into any problems during my playthrough that are Weapon mod-related. Please be patient, though. I'm playing on Insanity utilizing only a Mantis I and Predator I on my Infiltrator, so I'm playing VERY CAREFULLY with the chaos that is around me.
