I think the areas you are considering are outstanding, and I hope to snag some properties there myself.  

That's what the company researching the title does, so before closing you know about any outstanding liens.

After I made the offer the seller's agent told us the property is part of an estate and has an $81,000 outstanding mortgage.

You basically just answered your own question, when you move it to the LLC, you are selling it to that LLC. you would have a closing and everything because the Title would have to be changed, and there is a possibility that the " due on sale" clause will take effect and what ever you have outstanding on your loan, the bank could call due.

Has anyone bought a condo or town home in New Jersey subject to an outstanding HOA Lien?

The strategy is best described in Joel Greenblatt's fantastic book, and an outstanding practical guide and tool for executing it can be found over at the Magic Diligence website.You can do either (or both) of those using the "leverage" of Options, allowing for substantial upside potential compared to standard stock purchases, with dramatically reduced downside (if you want a no-hype education on Options, Erik Kobayashi-Solomon's book is great).Those with the patience and inclination can indeed use Option trading to make money in any market condition (Wikipedia founder Jimbo Wales, Amazon's Jeff Bezos, and "Black Swan" author Nassim Taleb all spent time -- and made lots and lots of money -- as options traders in their careers).For even more leverage, you could of course do any of the above (and much more) on margin (meaning your brokerage lends you money to do the investment), though that's not something I would ever do personally.Also, if you focus on holding stocks (or options) for at least a year, you benefit from favorable tax treatment of the profits.

Assuming that the due diligence checks out; paper trail is good, and it's worth substantially more than the outstanding balance and the payment history is as stated,  then you might have a good one here. 

This is what we look for regarding credit history.FINANCIAL/CREDIT HISTORY1.No outstanding debt to previous rental property owners.2.No outstanding debt to utility companies.3.No outstanding debt in excess of $1000 that is not in a payment plan.4.No excessive monthly financial obligations - more than 20% of income.5.Lack of credit history or marginal credit history may result in additional security deposit. 6.Derogatory credit (past due accounts, collections, charge off accounts, tax liens, judgements in excess of $1000 and/or bankruptcy) may result in additional security deposit or denial.

Update: the tenant paid $3000.00 of what is owed (the max allowed to be e transfered in 24 hours) the sheriff is still going today to post the eviction notice the outstanding balance is $570.00 It's a start, we did accept the $3000.00 as the landlord tenant board suggested.

Also, while the property is in outstanding conditions, only need new paint and carpet needed, monthly rent will cover the mortgage itself, very little ($25) as positive cash flow.