The flange is supposed to rest on the finished floor (but not higher). If it's up in the air, that's another story and would have to be fixed. Your toilet could be wobbling because the floor isn't level. If so, plastic shims from the hardware store will help.

Aiden - thanks for your response. I will have to remove a lot of the drain line to be able to do it properly, but it WILL be done right. Fortunately this section of plumbing is isolated from our primary bathroom, so I can take my time. And I'll be taking out some of the hodgepodged "fixes" they did before, so maybe this is a blessing in disguise. The guy is a licensed general contractor but he usually subs out his plumbing work. Wonder why! He didn't on our job because it was supposed to be so minor. Unfortunately he's already been paid, two years ago. I'm doing the rest of the reno myself. I've had 2 babies in the intervening years so it's been slow going, made slower by the fact that I keep having to re-do stuff that they did wrong.

Toilet installed and operational. I decided to put the wax ring on the toilet and set on the flange as a unit. This toilet is a low cost Glacier Bay from Home Depot and has a lot of quality look and feel and evens some "extra" parts. For one thing the closet bolts came with push on plastic washers that I used to hold the bolts vertical while I lowered the toilet. This is the first "extra" parts. Then on mounting the tank to the base the supplied bolts had the expected high-quality rust-resistant materials, and had the usual screw slot head inside the tank followed with a metal washer and a 1/8" (or so) rubber (or similar) washer. Then for the other end were the matching metal washer and nut. But, for some reason, more extra parts, regular steel-looking elongated washer and wing nut. The instructions did not go into detail on what this was for, but as it came in the package on the end of the closet bolts, I added them to the underside of the toiled lip...suppose they operate as a "lock-down", but whatever, I've never seen this arrangement before. Again, this is a very low cost unit, I'd expect fewer parts, not more. So far, so good.

It's best to raise the flange, and if you have PVC or ABS, it's not that hard. On the other hand, assuming the existing flange is resting on the original floor, you could install a couple spacer rings (HD has them) onto the existing flange, making sure to add some wax or silicone between the layers and then screwing them down snugly. Keep in mind that the flange should end up at the level at which it would rest on the finished floor. If it's still a little low, you could install the toilet with a jumbo wax ring. One other way might be drop in a flange w/gasket, that slides into the existing hole, but you need to make sure the gasket is snug (seals out the gases) and that it rests solidly on the new floor. HD has that, too.