Wow, ok you sure didn't ask an easy question for your first one!!!
What you've described sounds like its being caused by an improper A/F mixture. Now as to why that mix is off is going to require some troubleshooting.
There are 3 basic areas that could be causing your issues:
1) You could have an air leak causing the engine to run lean, VERY BAD
2) Your reeds could be worn or bent and would cause hesitation and stumbling but hopefully no real damage.
3) Your mixture screws or carb could be improperly adjusted/tuned
Numbers 2 & are the easiest to test for and fix so lets start there.
-For #3, pull out the spark plugs and look at the electrode base. What color is it? Can you post a picture of it so the color is visible. If the mixture is correct then the base will be a chocolatey brown. I don't expect this since that would mean you shouldn't be have your problems.
-For #2, remove the air filter and while the engine is running or cranking put a rag or paper towel near the carbs throat. If the reeds are ok then there shouldn't be any flapping wich would indicate pressure venting back through the carbs.
If the plug colors are off, then adjust the carbs. Too dark and you should lean out the mixture, and too light would go the other way. If the reeds are damaged then you'll need to pull off the manifold and replace them.
If neither one of those fixes work then you'll need to start looking for an air leak into the engine. This isn't terribly hard, just time consuming since the best way is to remove the engine from the ski.
To test for an air leak you need to pressurize the engine once you've sealed off the intake and exhaust. The engine should hold 10psi with now more than a 1psi per minute loss. Anymore than that and you have a significant leak. To find a leak pour soapy water on the engine while its pressurized and bubbles will show where you need to fix.
Thats a basic run down of what you need to do... There is more info available but I don't want to type it unless you need it, so just ask...
"Build a man a fire and he's warm for a day, but set fire to him and he's warm for the rest of his life!" - Anonymous