I have Mjoll as my follower, I noticed that recently whenever I drop stolen items (usually wrongly flagged) and retake them, Mjoll would say "I saw you do that" and all the stolen stuff in my inventory are confiscated, just like being busted by a guard. Sometimes she would go further to report the "crime" and add a bounty to my head. Worse still, the seized items are not in her inventory, we are in the wilderness and I have absolutely no idea where to take them back. Is this supposed to happen or is it some kind of bug??

Mjoll is pretty much a do-good kind of person.
I'm not sure how she knows that those items are stolen though while in the wilds, games can never be perfect.

Mjoll HATES the thieves guild, so there you go. If you want to be a successful thief, find a different follower, or if you married her, leave her at home.

Yes, but then you have that doofus that follows her around at your house

You might want to sneak attack him then, she won't know most likely that you killed him.
hmm...i should try that.

I did that, didn't work. Some how she knew it was me....he is kind of like a few of my in-laws

if married, "persuade" her to give it back... if you know what i mean. just make sure Aerin (the doofus) isn't watching.
jk lol.
She's programmed to rat you out for even the smallest crimes, unlike Aela, who will ignore crimes you commit while she follows you
to deal with Aerin, a sneak attack while Mjoll is busy will suffice, just don't get caught or she'll get very pissed at you.
if you recruit her into the Blades, he'll participate in dragon fights, and he's way too weak for that. he's suicidal?

apparently Mjoll is very accurate with staves

That's hilarious.

I got arrested in Markarth once, the thing is though, I knew what I was doing was going to get me arrested so, I gave her all my stolen goods before doing what I did in front of the guards. She happily took them without saying anything. And when I got out, she was waiting there for me with my stolen goods.

This is why i love Mjoll as a spouse and dark brotherhood initiates as a companion.