Started part time while working a full job at the County Sheriff's....then grew to full time slowly and went to full time beginning the 4th year. I didn't do a lot of advertising mostly because I was too busy working. The toughest time was when the business needed me full time and my other job still needed full time. I worked nights and mowed all day - crashed a few vehicles from lack of sleep - I was a crazy nutjob workaholic with like 3 hrs of sleep a day. Not sure how I lived.
Big mistakes? hmmm. I would say not planning and expecting growth. If you don't know already, then take some classes on business or at least start reading books etc. Expect the growth and plan on how much more you will take on each year and how much more equipment/employees you will need to manage that growth correctly. Also, decide who you want to market to and what your image needs to be. Do you want to run a big business, a small business, or work for yourself and just bring in some extra money?
Buy commercial equipment - nothing compares and you will be taken much more seriously.
Cash flow is tough when you are starting, but if you have another source of income it won't be an emergency. As hard as it is sometimes, be tough on any customers that pay late or fall behind. If you let them by now, it will only get worse. Just be sure to keep finances separate so you find out if you are making or losing money.
If you aren't too mechanical then start learning. Having a few extra parts at the shop and fixing something yourself in 2 hours is FAR easier and cheaper than taking it back to the dealer and being down a day or two.
Put together a schedule for mowing and maintenance jobs, give each job a specific day and time slot each week. Plan on 4 or maybe 4 1/2 days of nice weather each week and fill those days with 10 hrs of work (just my recommendation).
Do not take on "one time mow jobs" or "on demand" mowing. They will call when it gets 1 foot high and expect you to rush over on the one nice day you get all week and make it look great. Personally, I don't offer every other week mowing except for a very few customers - but that is up to you.