I own property with a 30ft red line on the map that has been there since 1943.

I’m also open to nearby areas like the Red Bank/North Shore border.

For me foundation issues are a red flag, but if you factor in foundation repairs, and the numbers still work, then it’s not that big of an issue.

If for instance you are leaving a much larger home and down sizing on the next home, this can be a red flag. 

What are red flags that would signal ‘this is a terrible deal/rate/terms/they are crooks’?

And that there are strict rules you must adhere to or else it sends up red flags?

If you have to think twice about the monthly holding cost, that is a red flag.Unless you're getting the home at a discount, I would look elsewhere for your first investment, preferably something that you are at-least breaking even on.

How big of a red flag is this?

Shouldn't raise any red flags under a certain dollar amount coming in (usually it's one large transaction, or in the amount over $5K that gets held for verification by the bank's holding fees - again National Anti Money Laundering laws)  but if you needed to leave it set for a few days until it did clear, still shouldn't be an issue unless you're using these funds for immediate use. 

The work may have been completed without permits which can be a major red flag and could cause problems in the future.