will I have a problem with worms or slugs? If so, what's the best way to deal with them?

worms love it, slugs don't

Just make sure to mix it into the soil well. if you dump coffee grounds on top, it will create a moisture barrier and dry out your plants.

Coffee grounds & strong coffee can eliminate destructive slugs & snails in your garden.
A study in the journal Nature found that slugs and snails are killed when sprayed with a caffeine solution. (1) Another study found that "After 96 hours, all of the snails treated with a 0.5% or 2% caffeine solution were dead." (2)

Lightly sprinkle coffee grounds & your leftover coffee around the base of plants, on mulch, & on edges of pathways to get rid of slugs & snails. Gently mix grounds into the soil if they start to accumulate to avoid crusting.

Earth worms, which are beneficial, will enjoy the improved texture of the soil that has coffee grounds added to it.

MI don't know a lot About gardening,but my mother- in- Law has the most beautiful plants you'll ever see.She uses both coffee grounds and egg shells in her soil.I'm not sure about slugs,but worms actually help fertilize soil.♥