I've been investing in residential and commercial real estate for over 10yrs and have learned from a lot of decisions along the way.
Certainly depends on the type of property, type of investment, and structure of the transaction. For example the answer would be very different between a SFR and a 200 unit apartment complex.
I always start with the macro - what is driving people to rent property in that part of the city. Will the reasons people are renting there continue to support future rentals and future rental increases (jobs, development rules, pricing, etc.)
If I like what I see for that city and that part of the city from a macro perspective, I look at the economics of the property itself (price per unit in relation to deferred maintenance, does the NOI pencil out to what I need it to be, is there upside in rents or utility bill backs or appreciation, am I buying at a discount due to deferred maintenance or lease risks, etc.)
Then I look at the structure of the deal itself - if I am leading the investment and have LPs, what is the rate of return for everyone involved. What is the holding period, plan to sell vs. 1031 exchange, etc.
Some of the areas where there can be difficulty is on deferred maintenance that a seller is unwilling to compensate you for (negotiation techniques are your friend here). Issues with the leases (some might be easy to overcome and others may not be). Financing (will a bank want to own that type of property in that city).