In the musical, Mrs. Meers's acting is even more cliche than in the film. Then again, Bun Foo and Ching Ho are pretty stereotyped too. So maybe her acting talent really is quite good In-Universe.
Another variation could be that Mrs. Meers actually ISN'T a good actor seeing how she was envious of all the other actors and blamed them for her past acting failures, and that the only reason she can fool the girls is that they're all idiots.
In the musical Thoroughly Modern Millie, I was always bothered with how Mrs. Meers seems to suffer massive VillainDecay in the second half. She seemed to turn from a threatening villain who sold people into slavery, into a reject choir girl. Watching it again, I realized that indeed, this transformation does indeed happen... but there's no indication that any of her victims are ever found or rescued. In other words, she has shipped off perhaps hundreds of young girls, mostly orphans, to be unwilling prostitutes in China, a country with people they cannot communicate with, because of her "reject choir girl" reasons. Alright, Meersy. You get your villain status back. - Hueha
Actually almost everything in Thoroughly Modern Millie is Fridge Brilliance. When it's revealed at the end that Jimmy and Miss Dorothy are not only brother and sister but Muzzie's wealthy step-children whom she cut off financially. It explains everything, how Dorothy was supposedly raised in an orphanage but extremely Rich in Dollars, Poor in Sense, how come Millie saw Jimmy and Miss Dorothy together, etc.
Why the heck would Muzzy (in the musical, at least) send her children out into the world with nothing but $25 and tell them to pretend to be poor? Because that's how she met her husband.
Fridge Logic: How does Jimmy get down from the Sincere Trust building's window ledge when he's "hundreds of feet in the air"? In the musical, the scene is immediately followed by a blackout. Was rock-climbing one of his hobbies...?
It had to have been, how else did he get there without going through the doors?