What are some of the common mistakes singles make when getting a resale HDB unit?

In my experience, the most common mistake is getting shocked by Cash Over Valuation (COV). While it's less common than it used to be, COV does still happen.

This is when you agree on the price, get the Option, etc., and then HDB reveals a valuation lower than what you agreed to pay; such as you when you agree to $350,000, for a flat valued at $345,000. The COV of $5,000 is not covered by your housing loan, so you have to pay in cash.

Again, it doesn't always happen, but have something set aside just in case.

As to Kembangan versus Bedok, I took a look at prices to see how much the scarcity helps.

Flats in Kembangan averaged $406 psf in end October 2010, and averaged $464 psf in end October 2020. For Bedok, it was $405 psf in end October 2010, and $422 psf in end October 2020.
It is not necessarily easier to sell a flat in Bedok by the way! If you like, do let us know the units or blocks you're considering, so we can get a more detailed view. It's always best to compare the specific units or blocks, rather than go by the general location.

Go for pte if you could afford. Else get a BTO if your are first timer or at least sale of balance flat. Singapore is not far from anywhere for its size. Buying resale HDB is a bad idea if you intend is not to stay long. Actually there are more options, DM and I could share with you. No obligation just wants to help