I've encountered another couple of bugs, I'm afraid. Firstly, a minor bug - if you do Platform Arena third, go back without using a teleporter and then do the Smart People level fourth, you'll get the congratulatory message for the Smart People level, along with "One remains", and then you'll speak to Vita and Vitellary. If you then use any teleporter and come back, you'll get the congratulatory message for Platform Arena along with "One remains" again, Vita will still be there and you'll have the normal conversation with Vita (which is mostly the same as the conversation with Vita and Vitellary, except it automatically sends you to T1).
Now, the slightly more major bug. I did Plaform Arena third and Smart People fourth but didn't use an extra teleporter, thus skipping the congratulatory message for Platform Arena. After the Polar Dimension and secret area, I went back to TA and back through the Platform Arena again - and ended up with 22 trinkets. So for some reason the game allowed me to get the bonus trinket for a second time. I haven't looked at the scripts to determine a cause. I'll try a couple more things now.
Having 22 trinkets means two things - firstly you can skip one of the existing trinkets, and secondly your unlock file will say your highest number of collected trinkets will be 22. (In case anyone didn't know, collecting trinkets in a player level counts towards unlocking jukebox songs in the main game, as it saves the highest number you collect.)
EDIT: After a brief test, I seem to have found out that Life Factory makes the Platform Arena bonus trinket available again. I did Platform Arena first, then the Maze, then warped to TA and couldn't get it. Then I did Life Factory, warped to TA and did get it. I'll try a few more things. Maybe a flag is set in Life Factory that makes this trinket re-collectible?
EDIT 2: OK, the bonus trinket can be collected INFINITE times. Simply set the teleporter to T3, warp there ("There We Go!"), warp back, warp to TA and go back through Platform Arena. Every time you do this, you get an extra trinket.
EDIT 3: More fun. If you manage to get 21 trinkets before going to the Polar Dimension PS for the first time (get 19 before entering the Dimensional Tunnel), it skips the whole destabilising thing, and you end up back at the ship with a glitchy text box showing four lines of internal script, then the script stops leaving you on the ship. (Skipping the bit where you'd normally speak to your crew then go back to read a letter from Vita.) I'm also thinking that a side effect of the glitch may be that using T3 after collecting this trinket makes the game think you've not collected the bonus trinket, therefore it would only expect you to need 20, not 21 at the final PS. I've not confirmed that, though. A cursory look through the scripts makes me think this isn't the case, but I'm not sure. It's worth checking, though. I think the possible cause is that using T3 from Life Factory sets flag 99, which in turn allows you to get that bonus trinket since that's the flag checked when deciding whether to award it. I'm also assuming that the normal check inside the Platform Arena which decides whether to set flag 99 won't normally set it if you've already collected the trinket - but T3 sets flag 99 unconditionally.
Oh, and Tunnel T8 sets 99 too. I think you need to make sure that the trinket can still be collected if you don't get it straight away - let's say you come back later to Platform Arena, you should still be able to get it - but only once. So another flag might be required to ensure it's only collected once. And it's clear that Flag 99 is being used for two different things.