Know what the rents are and ask your agent to run rental comps to make sure they are where they are supposed to be. I'd also pay particular attention to the roof and any AC units. Another good thing to know would be who pays the utilities. Also look at the neighborhood, the less other multifamily properties around you the better the neighborhood generally speaking.
@Katie Jewell Look for any deferred maintenance that will create costs immediately after purchase. Also look at things that may be detractors, like the neighborhood, or awkward layout, or tight hallways that will make moving furniture difficult, etc.
My main advice would be - Don't get lazy. Make sure you do a walk through through each unit even if its an inconvenience for the tenants. 8/9 rooms will be fine and you'll call it a day just for the 9th room had mold / leak/ something terribly wrong going on. I've heard lots of horror stories from new investors on this.
Is this an as is purchase?
Windows! Single? Double? Serviceable or not? Rot? Moisture between panes?
How old is the place?
Before offer check how old water heaters, furnace/ac, age of roof. During walk thru look under all sinks for leaks/signs of leaks.
If this is your first purchase I would recommend hiring a home inspector to give you a detailed report while under contract. Make sure you have an inspection period. Review leases, ask tenants if they like the area, how long they have been there, and if they plan on staying (if their units are clean and you think you would want to keep them). Look at tubs to see if there are cracks if fiberglass or rot/rust kn steel tubs.
Good luck and happy investing!