Say I have a Blinkmoth Nexus and Steel Overseer out. I tap the Steel Overseer for his ability to put +1/+1 counters while my Blinkmoth is a creature, and it gains a counter. After my Blinkmoth goes back into a land, does it keep the counter, or does it lose it?
Lands (any permanent, really) can have +1/+1 counters just fine. In fact, Llanowar Reborn enters the battlefield with one! The counter(s) will not go away just because your blinkmoth stops being a creature.
Of course, the +1/+1 counter doesn't do anything until the land becomes a creature again, but the +1/+1 counter will still be there.
It keeps them because nothing removes them.
There are only three instances when counters are removed from objects by the rules:
That's it. Counters are never removed from objects except in those circumstances or by abilities that instruct you to move or remove them.
There's definitely no restriction about which type of counters can be on which type of objects.