Would this be a reason to fail on the state inspection? Do cops bother you or no?

U will pass as long as you don't have a check engine light on.. U will get harassed if u get stuck in a mobile inspection.. like I did..

never gotten botered with mine

That's good news

Besides bat' installers, anyone got a reputable shop to install vinyl ovelays in central jersey?

As long as you are not covering the illuminated sections of your tails (reducing the amount of light emitted), you'll be just fine.
MA inspections can be a real PITA as well but I've never had trouble with mine.

good luck installing those.. i threw my set away as there a pain in the butt to install n fade over time... i ended up spray tinting mine the way i wanted n clear coating to make it shinny and it looks way better in my eyes in person then the bats... i tried to install bats on 06 taillights n it wasnt happening no matter what way i tried, but it might be easier on the flat 03-05 tailights

^^^^ thats the sexy right there

if you block the reflectors in the rear it is illegal

good looks on those tails scootch