Pallet adhesive is pretty gross. It inevitably makes some kind of mess, which can be anything from a mild irritant to so bad that it wrecks your press. However, it is a necessary evil. The purpose is to hold the shirt down on the press so that it doesn’t move or lift. Any moving or lifting will cause registration problems, the obvious problem. However, also look for poor release of ink through the screen as adhesive not holding the shirt tightly down will also have an effect on that aspect of printing. Not enough adhesive or poor adhesive will cause registration and printing problems, but too much adhesive or too strong an adhesive will cause problems. Signs of too much adhesive or adhesive that is too strong will be prints that are stretched out of shape from pulling them off the platen and sometimes the adhesive can leave marks that show through the print.
I have actually consulted with big shops where adhesive was one of the major problems, primarily causing registration problems.
At our shop we primarily use Albatross brush tac or roll tac and we apply it with a foam paint roller. It has the best balance of effectiveness, environmental responsibility, ease of use, and cost.