I found I had difficulty picking up large alien weapons - the ones that take up 8 squares such as the Plasma cannon (IIRC) and Particle Beam Rifle.
I had sold off some spare equipment & didnt't realise I'd equiped one of my crew with one of hte no-longer-existing weapons, so he started the game without a primary weapon.
I had him use his secondary, but got to an alien corpse and tried to pick up the Plasma cannon and it's ammo - the ammo was fine, but I couldn't get the gun to stick.
I had no shortage of TU's, and 2 empty hands. the right hand highlighted when I clicked on the weapon, as did the back-pack. I could put hte weapon in the back pack without bother, but not in hand.
I had researched the weapons (both of those mentioned above) and others in my crew are using them.