Frequency - How often do you want the lawn mowed? some companies only offer weekly mowing packages, but others offer mowing every 9/10 days or every other week as an option. It is also a good idea to ask what the policy is when the weather is dry and to ask how late into the year the company generally mows.
Pricing - How much are you going to be charged & how are you being charged? It may vary - It could be a monthly charge for "x" months or it could be charged "per cut". Once you are quoted a price find out what the billing options are. Some may offer a discount for email billing. Most should offer some sort of a discount for seasonal prepayment. Do not be afraid to make a counter offer - it doesn't hurt to ask for a better price.
What does the service entail? - make fair comparisons - a company way offer a better price simply by providing a lower level of service. Do you want the grass bagged? Is trimming included? Edging? Blowing off walks, patios, drives & decks? Weeds in walkways & driveways taken care of? Is the curb kept clean? Decide what level of service that you expect and make sure that it is included ion the quotes that you get.
Customer Service - Did someone answer when you called for a quote or did you have to leave a message? How long did it take for someone to get back to you? How long did it take for someone to come by & give you an estimate? Can you contact the lawn service by email? by text? Smart phones make it easy - an hour or so should be plenty of time to get a response or a callback. How you are treated before you are a customer may say a lot about how you would be treated as a customer.
Research - There are many places online to find more information on a service business (ratings,services offered , how long in business). The Better Business Bureau (example) is one. Angie's List is another. Take advantage of free resources that are available.
Insurance - Any service provider that you hire to do work on you property should be insured. Most companies will be able to show one page certificate of insurance (showing what they are covered for) when providing an estimate.
Other considerations - Are the employees uniformed? Is the company truck lettered & clean? People that take better care of what is theirs may take better care of what is yours. Do they use commercial equipment? A lawn mower from a box store will work well for mowing 1or 2 yards a week, but may not be reliable enough to do 20 or 30. A person that has invested in the right equipment may be a factor in showing reliability.