There are a few teamwork feats like Enfilading Fire and Coordinated Shot that pretty much do nothing because they require a character to be in combat with an enemy or to flank an enemy. Generally speaking though the guys that are going to be in combat with the enemy won't have point-blank shot or precise shot which in the case of Enfilading fire are prerequisites.
Aside from just reworking how teamwork feats work I think it'd be a good idea to add a new feat that would allow an ally to provide the benefit of the teamwork feat to their ally who does have the feat while gaining no benefit themselves. Require the feat to spend some time every so often training with that ally and limit the number of feats they could provide benefits for.
This is an idea of how this may work.
Battle Buddy (Combat, Teamwork)
Benefit: By spending 8 hours training under an ally with a teamwork feat you may count as having that feat for the purposes of granting benefits to your allies, you can only grant benefits for a single teamwork feat, if you train to grant benefits for another you no longer grant benefits for the previous teamwork feat. At fourth level and every four levels thereafter you can grant benefits for another teamwork feat without losing the previous.