There were a few Service Bulletins for the GX620, and some may or may not apply, depending on the serial number.
1. Air Gap: The ignition coil air gap to the flywheel must be set correctly, 0.4+/-0.2 mm (0.016 +/- 0.008 in.) Loosen the coil, place a long, flexible gap/feeler gauge (set to the proper thickness) under the coil, press and hold it against the flywheel, tighten bolts, remove gauge.
2. Spark Plugs: If run at low speed or under light loads, the original spark plugs may foul, or the engine oil may become fuel-diluted. First, be sure to check the oil level with the dipstick. Next, a hotter plug may help: NGK BPR2E2.
3. Later GX620's (serial 2007986?017570) had some failed rivets holding the decompression parts to separate from the camshaft. A new camshaft with improved rivets may be required. Only engines within the range are affected.
4. Later GX620's (serial 2000000?037853) may have cylinder #2 exhaust valve lifter issues. You can remove the valve cover, manually rotate the engine, and confirm if the exhaust valve is working. An improved lifter assy. is available if the old one has failed.
FYI, OTHER model Honda V-twin engines had an Emissions Recall for the ignition coils, but the GX620 WAS NOT part of this project.
If you'd like copies of these bulletins, drop me a PM with your email. If you are taking the engine back to the shop (and they are a Honda dealer) tell them to check Engine Service Bulletins #15, #19, #27, and #29.