"She knew that the carpet is dirty."

Translation: Ona wiedziała, że dywan jest brudny.

[Arnoldpitt]

Is this another example where not only the ending but the stem changes in the imperfect?

[alik1989]

Wiedzieć doesn't have a perfective stem, and I don't understand what you mean by "stem changes in the imperfect".

The past conjugation is irregular. There is an -ie- <-> -ia- alternation in the plural.

I think wiktionary will answer most of your verb-related questions.

[2nail]

How does she know that the carpet is dirty. I can understand her knowing it was dirty. Unless she has a gift of seeing into the future.?

[domnelson]

Because it was dirty then and it's still dirty now...

[dmkusner]

Would 'znała' work here instead of 'wiedziała'?

[alik1989]

No, znać must always take a direct object.