I thought it would be easy peasy but it looks like the HOA is about to reject my application because they don't want me renting it straightaway.

Besides the fact that I am not in the same country as the buyers and communication with these unknown people would be difficult, the title company representative who emailed me of the error provided completely erroneous figures for the amount owing, and now we do not know what the taxes actually were that were applicable to my time living in the house (just prior to and for nearly a year after my father´s death).

We do a full background check on all applicants--is there anything you'd like to discuss with me?

I do want to let you know, there are numerous meetups in and around the Philly area just like @Mary W. and @Sheryl Sitman mentioned.

Would it simply be a matter of them re-filing a tenant application?

It means nothing.Pay $5,000 to "Open the Door" and you have bought a black box of whatever the seller wants to provide (a paper application handed to you from a lender, a website address, etc...)When buying something like this and "Sales Fluff" is introduced into the conversation (vs. hard facts such as, a line of credit will be set up for $X 90 days after doing Y with Z lender, etc...) there is unusually a reason for the "Sales fluff".Ask for a copy of the contract and take the time to read it to see what you would actually get for your $5,000, and if the contract has "Sales fluff" in it--Buyer Beware.If there is no contract, or they balk at giving you an opportunity to read it (pressure you into signing now), it might not be such a good deal for you.And Sales fluff may be a red flag about other parts of the "Opportunity" also.Good Luck! 

It’s taking a little longer to rent out, which is making me wonder whether something wrong with it or whether I need to keep waiting for the right applicant to come along.

There's so much information out there nowadays and one may as well utilize it to help with the screening process.Letting applicants know up front what your vetting process is will help weed out some as they'll seek an easier target.

I find a single mom of 1 that loves the place and submits an application. 

She submitted her application and passed all of our qualifications (income, rental history, etc) When I reminded her that everyone over 18 needs to submit a separate application, she informed me that it would just be her and her two children living there.