what does it mean if your cassette deck playback and recording sounds warbly?

That's wow and flutter and if you hear it on all your recording send the deck back it's not working right. If it's just a few it's on those recordings it happens.

"...what does it mean if your cassette deck playback and recording sounds warbly?..."

Your deck sucks worse than the cassette sucks. 

First use some alcohol on a clean cloth to clean the capstan and pinch roller. You do not want to be using alcohol long term but this is just to check and eliminate one possible cause and so for this one time no problem. If when these are perfectly clean the problem persists, and if it is on all cassettes, then the unit is defective. Probably a bent capstan, or a bad pinch roller. Either way, back it goes.

Belt? It’s like 101 on a cassette player..
MC got it... Clean and inspect..
Retention your tape.
Go all the way one way AND all the way the other high speed of course.. It helps.

I like cassette, don’t like the play back to much, though.. :-)

I’ll put one in the playback rack.. Tascam for cassette, Otari for RtR
Both affordable and available..

Regards