Or any bills for that matter?
IMO: serial # always trump plate numbers (for collector appeal) since these are much more noticeable & are unique for each note (much like a fingerprint). "mtuma3" provides some great examples of desirable serial numbers that most collectors seek.
Plate position numbers can also affect US $1 Book Value (BV) which were printed by "Web press" & for "Mule" notes. I first learned about these on Youtube & found some UNC Web press notes (printed in 1988A, 1993 & 1995) all of which can be identified by where the back PPN are printed. If you're interested in these I suggest you use "web press notes" and search for a more explicit explanation (or maybe someone can jump in here?) If you want to collect these - then I suggest you try to find (buy) UNC examples as there are many who will hoard circulated examples & they (like replacements) just never go up much in value (the perils of being a FB/Youtube collector).
I believe "mules" are excess front printed sheets which were printed & then matched with different back plates (thus having different back PPN). I am less clear about "mule notes" but they have existed for a long time & can be quite dear in older series. Again, you need further explanation, you can google or youtube for a video explanation.
As a Canadian, we had a few prefixes of our 1954 Modified Portrait $1 printed without a FRONT PPN and these all command a premium in BV. They were only printed for a short period (our RCMP stepped in as PPN's were seen as a necessary security feature) so quite tough to find.
Now one more observation about serial numbers:
If you branch into world notes you will also find that not all replacements have asterisks in front or behind SN but rather specific prefixes (like Z or X). If you are interested in these then check the catalogues. There are also test notes which have specific prefixes too (& can be quite pricey).
BTW: great question!