Dog crap: You find one the hard way, you either stop the engine, spend an hour poop scooping, and resume, and add it to their bill. OR you run the weed eater high enough to miss the crap, then explain to the customer later.
Slow payers. Explain the problem. Give them a range of choices:
A: Prewritten cheques for the season. Explain that there is a $50 charge for an NSF cheque, and that thereafter the business is cash only before work is done.
B: Pre-authorized regular billing on their credit card.
Other options: On the bill give 5% off for payment received in X days. 2%/month for late payment. Build the discount into your quotes. Make it clear to them that you want them to pay on time.
Register with paypal. They have a slick system for electonic invoicing.
Neighbors who cut their yard too short. Ask the client if you can lime the property line. Put a decorative line of rocks. Sell the clients a hedge. Sell the clients a fence.
PITA clients. Finish your contract and drop them. If you have a LOT of PITA clients YOU are doing something wrong.
People who complain about estimates: Extimate costs X dollars. Price comes off of first month's fees. Also: On your website, have a guide line to "How much is this going to cost me?" and have some typical scenarios and prices. Make the prices on your guide slightly high, so that when you estimate a job, you can come in 5-10% lower than what the guide said.
Come back a week later in the evening and have a chat. Walk the yard, and show them what the lowballer did. Leave your card and say taht they are welcome to come back. Also if the price is too high, have a proposal for a smaller number of services that would still be done to your standard.
People who interupt you. Have a tear pad of frequent interuption explanations, tear one off and hand it to them. But seriously, how often does this happen?
Other contractors. I've usually had no problem with this. Try to catch them as they pull up. Find out what they are going to do. If they need access, interupt your routine and mow a path for them. If they are there to work on the water system ask them to come back in an hour when you are done. If they are real pains, go away and finish later. Phone the client explain the issue and request that they call you when the X are going to be worked on, and that in the future there will be a surcharge if you and the other company can't work around each other.
Children nearby. Get a mower that doesn't throw stuff. Mow in a pattern that directs the debris elsewhere. In 20 years I have twice thown something hard enough and far enough to be a hazard to someone else. Both times I was cutting short, and went over a gravel driveway.
Explaining to customers about dumping. Build it into the bill. Don't charge them extra for it. Mulch mowing -- $40 Mow and haul away clippings, $50. Or bag it and leave it at the curb for the next pickup.
Work runs out. In the working season, automatically move $X per month to a special account for winter. Learn a new specialty. You've got a shop, you are likely pretty good at keeping things working, offer winter tuneups for people who mow their own lawns. Later you can make them your customers.
Depending on your area firewood may be a viable fall season enterprise.