Valuable feedback. There are few points I'd like to comment though.
I'm in favour of dropping additions "Wielkopolski", "Mazowiecki", "Podlaski" (for non-Polish speakers: those are adjectives indicating provinces the towns are located in, e.g. "Rawa Mazowiecka" = "Mazovian Rawa" = "Rawa in Mazovia") whenever possible, as most of them are modern additions and they take too much space, making the location names too small. The only case where, to avoid ambiguity, I would keep them is "Środa" - we have two of them on the map: one in Greater Poland ("Środa Wielkopolska"), the other one in Silesia ("Środa Śląska"). Ergo: I wouldn't change anything here. The current map is perfect in this regard.
Rawicz - you are right it should be renamed, however I find Gostyń to be the best choice, as it was definitely the most significant town in that part of the powiat (although it may require a slight redraw of the border, as shown below, as currently Gostyń lies few pixels north of the Śrem - Rawicz border). Since that border is not a border of a powiat, but an arbitral one, I would go for slight modification.
Buk - Lwówek was an intuitional choice for me too, but if you read more about it, you'll find that at the start of the game, up until at least end of 15th century, Buk played more significant role (Buk: town rights in 1289, Lwówek: 1414). Below I pasted an exempt from Codex Diplomaticus Majoris Poloniae (
https://www.wbc.poznan.pl/dlibra/show-content/publication/edition/7827?id=7827) presenting number of armed soldiers towns in Wielkopolska, Sieradz Land and Łęczyca Land were obliged to assembly in 1458 as a relief force for the besieged Marienburg castle (which we may use as an indicator of towns' size, wealth and importance). Buk: 15, Lwówek (Lwów): 12.
Mstów - case similar to the one above. Old town (town rights since 1278), the most important settlement in the area at the start of the game, that over the course of the game lost its importance. I would keep it as it is, partially also because it lacks a strong competitor (yes, Olsztyn you menitoned was granted town rights in 15th century and grew to prominence in 16th/17th, but was destroyed, burned and at the beginning of 18th c. was mererly a rural settlement, thus similar to Mstów it's glory was only episodical).
Putzig - just a typo, I know. It's not "Płock", but "Puck" in Polish.
That location with small font is "Neuenburg in Westpreußen" ("Nowe" in Polish).