Learn Russian: Что за мазня эта картина!

The phrase Что за is always followed by the nominative case when used to exclaim 'What a...!' or ask 'What kind of...?'. Both мазня (the exclamation) and эта картина (the subject) are in the nominative because Russian leaves out the verb 'is' in the present tense, so there is no verb to force a different case.

Where does the word мазня come from?

It is a colloquial noun derived from the verb мазать, which means 'to smear' or 'to spread'. In an artistic context, it becomes a derogatory term for a badly painted picture, literally translating more like a 'smear' or a 'daub'.

Can I change the word order to Что за эта картина мазня!?

No, the construction Что за must stay directly attached to the noun it describes or qualifies. You must group Что за мазня (What a daub) together, and then follow it with the specific subject эта картина (this painting).

How do I know this is an exclamation and not a question?

The construction Что за plus the nominative case is used for both exclamations ('What a...!') and questions ('What kind of...?'). In spoken Russian, your tone of voice makes the difference clear. In writing, the exclamation mark tells you this is an expression of strong feeling rather than a request for information.