Hi kriterrz,
You didn't mention if the broken firecrackers were just broken in two or if they were the remains of having been popped. Irregardless, I don't think there is anything to worry about. But if it concerns you, then remove the mulch. You won't need to remove any of your soil. Maybe he did it to stress you out!(Ah,sweet revenge!)At least you didn't find it filled with pieces of your cat! ;)
BTG

It does sound like a case of 'an eye for an eye...'.

I should think that firecracker waste should contain a lot of minerals. There should be potassium, phosphorus, magnesium and rare trace stuff -- shouldn't there?

His gift was a warning to you regarding the activity of your cats in his yard. I am presuming the firecrackers were not exploded and being broken in half would cause me think that his intent may have been to use them to scare off your cats out of his yard. You need to be responsible and a good neighbor and either confine your animals to your yard and provide them with an easily accessible place to poop on your property and not on his. He is entirely in his rights to have animal control take your animals.

I know of instances where the neighbor's cats simply disappeared forever.

very understandable---I love my cat, but really don't care for the cleaning up after the neighbors cats, or dogs in my yard and gardens, imagine planting seedlings and the "suprises" one pulls out of the raised bed when neighbors cat used it as a litter box?

its just a bunch of natural minerals like albert said,you know sulphur and the like.i was crazy like this about my first garden which was last summer.

Maybe he is hoping your cats will now use your mulch instead of his.