So if the mage complained that the Inquisition was doing nothing about templars who were known to have committed heinous crimes, would you have believed him?
Sure, provided he could prove it.
2. How do you know Cassandra hasn't done about the supposed criminals already?
I do not know, but her answer to the Templar was still bad.
She did not say "Don't tell me how to do my job." She says that Inquisition recruits having some criminal background does not matter and to just ignore it. I do not like or agree with that answer, regardless whether or not the recruits are mages. Taking in the wrong people can be bad in the long-run, no matter how desperate the early Inquisition may have been for recruits immediately.
If that is what she tells someone, then it is probably not too far off from what she is doing. After all, she missed Solas.
3. What about any supposed criminals on the templars? Surely you can't think that every templar you recruit is some innocent saint? Why does nobody call out investigations for potential templar criminals?
I said that the criminals being mages was irrelevant. Since you cannot seem to put 2 and 2 together, let me confirm that yes, any such investigation of criminals should include Templars and all other mundanes. What is odd about this is that Cassandra actually has a quest that deals with hunting down apostates *and* rogue Templars, yet she overlooks those very same elements possibly infiltrating Inquisition ranks.
Not sure if bad writing (easy explanation) or legit character flaw (this is not the only 'miss' on her part).
4. Why do you assume Solas has anything to do with what he says?
No one assumes that. Solas just happens to prove him right, and goes to show that the Inquisition needed to be more careful with whomsoever they recruited, lest they harbored criminals and let them loose to start making trouble again.