So I tested the item with a lot of other items and found a few bugs. Most are minor, but some are pretty game-breaking, (and not in the good way).

Tiny planet: Completely breaks it. Tears shoot off somewhere off-screen but don't count as gone, so you can't even try to shoot more.
Rubber cement: Tears damage enemies once but don't disappear, so you end up not being able to do any more damage. Being hurt and other things like enemies jumping makes the tears do damage again for some reason. You can also "recharge" your tears by having them touch a wall, where they'll try to bounce and end up spazzing a bit, after it they can deal damage once more.
Ludovico: You get only the ludo tear in the bar and is stuck right in front of Isaac's face.
Proptosis: Tears shrink too quickly for you to get an actual bar of tears.
Ipecac: Works as one would imagine, but it's a really bad synergy getting exploding tears so close to your face due to the slow firing rate.
Tractor beam: Graphical issues when moving the bar diagonally, could probably just remove the tractor beam graphics if possible.
Bob's rotten head: The bomb counts as a tear so it'll be part of the bar.
Piercing tears: Tears don't pierce enemies. Don't know if intended.
Continuum: Graphical issues when tears go off-screen.
Incubus: Fires regular tears, don't know if it'd be possible to code it getting a bar of it's own.
Cursed Eye: Graphical issue, you can't see the in what state of charging you are.

Despite this I still love the item, but I would just like to see some of the more game-breaking issues fixed if possible.