I don't think the rotational backlash when you change the spin direction (which is what I thik you mean by slap) is a big deal. When you rotate the spindle by hand does it rotate smoothly without rough or noisy spots? If so the bearings are probably decent. Does the motor run well? I wouldn't worry about the belt width as long as the rubber is in good shape.
The main thing is to check the alignment of the spindle and chuck. Ideally you can setup a dial indicator and measure the run-out on the exposed part of the spindle right above the chuck, shouldn't be more than a couple thousandths. Then chuck up something uniformly round (drill rod, transfer punch, or a drill bit long enough that there is a smooth portion to set the tip of the indicator on without it hitting the flutes) and measure the runout. If you've got runout issues at the spindle you may be able to adjust it (you'll have to google procedures for that drill). If the runout problem is at the chuck (much more likely) then replacement chucks are readily available. Most consumer grade machines come with less-than-accurate chucks anyways.
Of course the simplest test is just to try drilling some steel. See if the tip wanders around (use a known straight bit).
What speed ranges does it have? For drilling steel @ 1/4" diameter you'd like speeds below 750 rpm. Many drill presses won't go slow enough for heavy metal work.
I'd be inclined to keep it if most of these things check out. It's probably better made than most of the new machines you can find today.