If you're lawnmower is running unevenly, check to see if they are any loose wires. Also replace the oil and spark plugs. Make certain the under carriage is clear of all debris. Try adding gas stabilizer or additive to the gas tank.
Make sure the gas you are putting in it has no water in it you may even want to add a cap of dry gas but no more than that because it ups the octane level in the gas and make the motor run hotter. And check the spark plug.
It may need some common maintenance performed on it. Something as simple as replacing the air filter or the spark plug can help the lawn mower run smoother and more efficiently.
I would check the sparkplugs first. Also, make sure you didn't put bad gas in, or gas that's been around all winter. That can cause any lawn mower to skip.
When a motor is not running smoothly it could be bad gas, the line from the tank to the carborator may be plugged, or the carborator may need to be adjusted by a professional.
Your Honda lawnmower requires immediate wheel alignment and wheel balancing otherwise it will further intensify. Some accident may happen If you ride on it in the present condition.