#: ulanguage.rmain_lettersexchanged
msgctxt "ulanguage.rmain_lettersexchanged"
msgid "%d letter has been exchanged"
msgid_plural "%d letters have been exchanged"
msgstr[0] "%d kirjain vaihdettu"
msgstr[1] "%d kirjainta vaihdettu"

This will result in incorrect Finnish:
0 kirjain vaihdettu ->should be 0 kirjainta
1 kirjain vaihdettu ->OK
2 kirjainta vaihdettu ->OK

Finnish has only 1 as an exception, other integers: negative, zero, two and greater have the same inflection. How to do it right?
It's probably easy to phrase all of these so there's no need for more than one translation. Perhaps it is the best way.

I used Virtaal for translating.

The same happened also here:

#: ulanguage.rmain_calcresult
msgctxt "ulanguage.rmain_calcresult"
msgid "Only %d valid word found which score with"
msgid_plural "Out of %d possible words found the best would score with"
msgstr[0] "Löytyi vain %d sana, joka saisi "
msgstr[1] "Mahdollisia sanoja on %d, joista paras saisi"

->message during game:
Löytyi vain 291 sana, joka saisi 34 piste. ?????
->Should have been
Löytyi vain 291 sanaa, joista paras saisi 34 pistettä.

#: ulanguage.rmain_numberofpasses
msgctxt "ulanguage.rmain_numberofpasses"
msgid "Only %d pass left until game end"
msgid_plural "%d passes until game end"
msgstr[0] "Vain %d passaus vielä ja peli päättyy"
msgstr[1] "%d passausta pelin päättymiseen"

->In the message window:
Vain 7 passaus vielä ja peli päättyy
->Should have been
Vain 7 passausta vielä ja peli päättyy

This seems a lot of work to get one or two letters correctly where it even doesn't matter much. It worked in the old translation.

Actually, I have my own code for pluralization and do not use (n)gettext. Finnish is implemented as form1 in case of 1, everything else is form2. It's the same as in English or German. And those languages work well. On Transifex where I uploaded your translation all seems to be okay too: 1:%d kirjain vaihdettu, everything else: %d kirjainta vaihdettu.
I'd like to blame Virtaal... :-)