Buddy built my deck for cheap, but should the stairs have a landing at the bottom?

Not standard, and your instinct is right. Stringers parked on bare dirt is how you get a staircase that's wobbling in three years. Every rain, the wet soil softens, the bottom of the stringers sink a little at a time, and the wood that's sitting in that mud stays damp constantly and rots from the bottom up. The last step floating is a symptom of that allready starting, or it just means he never notched a bottom riser or set a proper footing.

The fix is cheap compared to what you're imagining. You don't need a big poured landing unless you want one. What most guys do is dig out the mush, put down a few inches of compacted gravel, and set either a small concrete pad, a couple of solid pavers, or concrete blocks under each stringer so the wood isn't touching soil. Even better, the stringers shouldn't really carry the load on the ground at all. They should be attached up top to the deck frame with hangers or a cleat so the bottom is just resting, not bearing. If his are just nailed to the rim and sitting on dirt, that's the lazy version. One more thing worth checking while you're out there: where is the water going? If the ground under the deck turns to soup every rain, the grade is probaly sloping toward the house or at least pooling there. That's the part I'd worry about more than the stairs long term, expecially with your AC sitting in that low spot. Standing water and mud around an AC unit shortens its life and makes the service techs grumble every visit.

I'd have him back for this one. It's an afternoon of work with materials you can buy for under a hundred bucks, and any guy who's 'built a bunch' should be able to do it without excuses. If he shrugs again, it's not hard to do yourself with a level, a shovel, and a bag or two of gravel.

This kind of hits home for me. Had a guy do a small deck off my back door a couple summers ago and the steps ended up resting on the ground too. Two winters later the bottom step was noticeably lower on one side and I had to prop it with a scrap of 2x4 untill I fixed it. So yeah, listen to what folks are saying here.

One thing I'm curious about though. When you ask him to come back, does that ussually cost extra or is it on him since it was his work? I felt awkward bringing it up with my guy and ended up just paying for the fix myself because I didn't want the wierd tension at the next barbecue.

If the stairs got the lazy treatment, check the main posts too before he comes back. I helped a coworker rebuild his deck two summers ago and found one corner post just sitting on a cinder block half buried in soil, no hole, no concrete, nothing. Took us an extra Saturday to jack the frame up and pour proper footings. Same logic applies here, a guy who shrugs off wet stringers probably cut corners everywhere you can't see from the couch.

Update: took the advice about checking the main posts and grabbed a flashlight under there last night. Sure enough, one corner post is sitting on a couple flat stones instead of footings. Texted the guy and he's coming back this weekend to set the stairs on pads and dig that corner properly. Guess I'll see if he actually shows.