Merrill manages to physically recreate an entire working Eluvian from a single tainted shard, which she managed to cleanse from the taint by herself. She only couldn't get it to activate once it was complete because she didn't have the magical password. That's like building an entire car from scrap parts, and only not being able to start it because you're missing the key. She clearly showes that she knows more about Eluvians than Hawke and Marethari combined.
Marethari herself showed complete ignorance of the Eluvian when she said it killed Tamlen and Mahariel, when both Duncan and Merrill said it wasn't the mirror but the darkspawn taint that killed them. Merrill herself cleansed the shard of the taint, and made a mirror that was clean and safe to touch.
Marethari herself also let Audacity out of its prison and let it possess her, which shows that she is responsible for letting it get out while Merrill isn't. Merrill made a deal with Audacity when she first met it same as Marethari, only Merrill's first deal with Audacity left it right where she found it nearly a decade later, whereas Marethari's first meeting with Audacity ended with it getting loose and possessing someone. Who's the bigger idiot where Audacity is concerned?
What's more, when Merrill intended to go talk to Audacity a second time, she brought someone along to kill her in case something went wrong. What did Marethari do? She went alone, didn't tell anyone where she was going, and let it possess her without a backup plan. Who's the bigger idiot where Audacity's concerned? Not the one who didn't let it loose, not the one who didn't let it possess her, and not who took precautions in case she might get possessed.