Title pretty much says it all: are there any type combos that resist no other types?
No resistances, and a four times weakness to Bug-type.
I don't know if there's anything else, but I'm nearly certain that's it. Closest is Water/Ice, with a unique resistance to only Ice-type.
Normal/- is immune to Ghost and 2x weak to Fighting.
Psychic/Dark is immune to Psychic, 2x weak to Fairy, and 4x weak to Bug.