Nice price - the Plex issues are Plex specific, as it's their SW in the QNAP App Center - not QNAP's problem directly (except perhaps for vetting that the code actually works).
The processor in the TS-231 is more than capable, and the TS231 has more than enough RAM to support that app - it doesn't perhaps do transcoding, but sharing files should be fine with Plex...
I agree with you that file sharing should work with the TS-231. The fact that it has good reviews as a FTP server, backup server, and dual gigabit LAN ports that can be aggregated or connected to separate networks is what sold me on this box for this price.
As for the Plex problems... All I can say is that the main header of the QNAP ads and the literature all state in bold lettering that this NAS works as a PLEX server. The QNAP forums, Amazon.com reviews, and NewEgg reviews all have references to this TS-231 not working well (Hang-ups and Lock-ups) when doing Plex server duty and transcoding files. Several reviews of the TS-231 point out the fact that the RAM is not really sufficient for large file transfers.
I have several desktops and servers doing Plex Media Server duty. I build Plex Server systems for friends and people who pay me to do it. I used to like the Lenovo ThinkCentre M58p or M81 small form factor desktops using the Intel 3GHz Core 2 duo processor with 8Gb pc8400 RAM and PCIe USB 3.0 cards. I set them up with Windows 7 Pro 64-bit OS on a 500GB HDD or SSD (if they want to splurge) usually but I am experimenting with Linux Mint. I can build those systems for under US$200 + the external HDD storage cost. Anyway. with the configuration above, the server will still hang-up when the files are .avi streaming to a Roku 3 media player. It is even worse when using the Google Chromecast or Amazon Firestick media players. If a 3GHz Core 2 duo has problems transcoding 720p or 1080p .avi files, why would the 1.4GHz (I think) ARM processor in the TS-231 be better?
I also set up Plex Servers on the Lenovo ThinkServer TS-140 with the 3.4GHz Intel i3-4130 and 16GB or 32GB of pc3-12800 RAM. That server has no problems transcoding multiple .avi files simultaneously and the cost of those boxes was under US$200 on sale (with 4GB RAM, no OS, no OS drive, and no HDD's). With a TS-140 having a Xeon E3-1225v3 CPU and 16GB or 32GB of pc3-12800 ECC RAM, I can simultaneously stream seven (7) different 1080p files of which 4 are .avi files without hang-ups.
As is usually the case, you get what you pay for. I don't expect the TS-231 to be a great Plex Server for that price. I will be happy to play around with it and see how it works for backup duties, file transfers, and accessibility from multiple networks. If it does that well, I will be satisfied.