Only thing better would be initial deposit and then paid in full upon Certificate of Occupancy and punchlist complete.Of course, standard items should also be checked: licensed, insured, willing and able to pull all required permits, reference checks.I would also commonly avoid the cheapest bid you get.  

I will often go against the common investor thought and defend my position based on my experiences.

One challenge that may arise during the sale process involves third-party property management.

@Rud Sev, I would ask the syndicators you are considering if they have any sample K-1s they have issued in the past to try to get a general idea of how they treat their common taxable items.There are a few things that are likely needed to be outlined:Your capital account balance for the investment, i.e. how much money the syndicator is saying you have outstanding at any time and used to calculate preferred returns, can vary from your taxable capital balance shown on K-1.  

Make sure everyone knows a cleaning schedule, expectation for common areas, how are you splitting utilities, guest policy, etc. 

I'm not sure if this is a local thing or if it's common in all markets.

To gain investor confidence, ensure the investment property numbers are real, use the most common contract forms in your state (versus a 2 or 3-page) internet/guru contract form) with appropriate addenda, or an attorney-drafted form and attorney-drafted assignment agreement.

@Jason Tucker  you need to add in your utilities, common area cleaning, and turnover costs to determine if it makes sense. 

Ideally, I'd like to find a balance between affordability and potential for appreciation.Also, are there any common pitfalls or things to watch out for when buying a multi-family property in Jersey City?

You should target states that have more common sense and people oriented government and regulations (hint-hint: stay AWAY from Dem controlled jurisdictions.