I will start this off and others can add their thoughts as appropriate. Our experience has been that the Mikuni carbs have been very reliable. However, with that said, in order to avoid problems this is the approach that we take with all new-to-us Kawasaki sleds that come into our possession:
1. Thoroughly clean the carburetor body inside and out.
2. Remove air bleed screw, remove idle stop screw remove needle jet, remove pilot jet, remove main jet, remove econojet.
3. Blow out all passages with carburetor cleaner and compressed air. We have even taken to using a small wire cleaner to make sure that the passages are clear of all obstruction. Clean the needle jet - there is a moat at the top that plugs easily. Make sure that this is clean and that the idle air passage in the needle jet is clear.
4. Re-install air bleed screw and idle screw. Set to factory set points.
5. Install new jets - pilot, main and econo to original factory spec [one caveat here is that we have our own mix for Intruders. Kawasaki used a different mix over the various years. We have settled on 25 pilot, 150 mail, and 120 mag/130 pto econo jets]
6. Replace needle and seat.
7. Generally no need to replace bowl gasket if it is not damaged.
8. Replace econojet hose.
9. Replace "O" ring at base of needle jet.
10. Confirm that the needles and slides match factory specification for model and year of engine. Find correct parts if the numbers are not correct.
I have probably forgotten something here and welcome other input.