If you have oil there, you might want to go ahead and order a stator side main seal and a flywheel puller (the little nut thing). Be specific when looking/ordering;stator side and clutch side are 2 different sizes IIRC.
If it's really bad, it might give you the symptoms by itself. At low RPM, the crank pressure ATDC and before BDC won't build up enough to keep all of the gasses moving and the gas will fall out of the air. After a few minutes, the bottom end can become saturated, giving you a lean condition initially (before it becomes saturated) and a rich condition afterward.
On top end, the gas can clean out, but you'll have a lean condition because you're sucking air. If it's really bad, you'll rev fine but it'll seem like it hits a wall well before it should.
The other possibility is that the previous owner was either sloppy or new to carburetors and screwed the floats up. Take the inlet tract off of the back of the carb and turn the gas on. If you have gas leaking out of the overflow, your floats are set wrong or you have trash in the gas. Keep in mind, a piece of hard trash that's so small that you can barely see it will cause the valve to malfunction. Obsessive cleaning will do more than visually checking for any trash. Now if the owner blocked the overflow off or if it's clogged, you'll pour gas out of the needle seat.
You may also want to check the stator and CDI resistance if it's a "rev-limit-ish" cutout.
Also, go ahead and get some dawn dish washing liquid. Take your tank off, drain the gas, remove the petcock and place it in the tank, and add a touch of water. Add detergent, shake profusely, add water, shake profusely, drain water, rinse, repeat until you're sick of it. Then, take the petcock out of the tank and clean it repeatedly. Stick your vacuum cleaner hose down in the tank and leave it for a few minutes. Take the tube out and spray WD-40 in the tank. Spray carb cleaner (2 bottles should be more than adequate) in the tank until you're convinced that it's dry. Re-install the tank and add gas. If you have an inline filter, replace it. If you don't, get a motorcycle inline fuel filter and install it. Don't be tempted to get a Briggs and Stratton fuel filter. They clog easily.