What exactly is included in a visit? This is the question that prevents most disputes. Mowing alone and mowing with trimming, edging, and blow-off are two different services at two different prices. Get the list in writing, and get it before the first invoice rather than after.
What day will you be here, and what happens when it rains? A crew that can name your service day is running a route. A crew that says 'sometime that week' is fitting you in around whatever else comes up, and you'll feel it in July.
Is the price flat or does it change? A flat per-visit or per-month rate should stay flat. Ask directly how extra work gets handled: it should be quoted first and only happen if you approve it.
Who is actually doing the work, and is it the same people each week? Continuity matters more in landscaping than most people realize. A crew that already knows where the sprinkler heads, the soft spots, and the property lines are will do a better job in less time.
What happens in the winter? A company that only mows disappears in November, and you're finding a plow service in a snowstorm. Ask whether they run year-round.
And finally, can they tell you what won't work? A landscaper who says yes to everything you suggest is selling, not advising. The person worth hiring will tell you when a plant won't survive your exposure or when a bed is in the wrong spot — before you pay for it.