I like how you manage to find positives in this serial, which apart from the Rani's first appearance is fairly inconsequential. It plays a bit like a series of preposterous events happening while the three Time Lords have a reluctant reunion in 19th century England.
Although it's tempting to pick the story's faults apart, the reasons it does hold together are mainly a) the authentic setting that ooze industrial revolution atmosphere (the Ironbridge Gorge museum where it was recorded has since become a UNESCO world heritage site), and b) the strength of the main actors that carry the ramshackle story through.
I do believe this is the first time I rewatched a Colin Baker serial... they don't really beg for repeat viewings in themselves, but I realise that isn't in any way to do with the lead's talent. The fact alone that he pulls off wearing that coat is impressive. Lesser actors would have become second fiddle to such a wardrobe.
Arthur Ainley did ham it up as the Master — it's safe to say the broad vaudeville traits of the character originated with him — but there is also measure and some restraint to his work. It's against these two that Kate O'Mara really gets to shine as a new character that has implied back story with them.
O'Mara clearly has fun stepping into the eatablished conflict between Doctor and Master, and into her part of a grade A mad scientist — not clinically mad, but totally unscrupulous with no regard for the consequences of her work. As the Rani, she is obviously frustrated having to deal with the indulgent schemes of the Master.
Everything outside of that ménage à trois seems to be afterthoughts to keep Nicole Bryant and guest stars busy. Peri gets a few outstanding moments during her time in the TARDIS, but not in this two-parter, unfortunately. The Master has some nefarious plan to prevent the industrial revolution(?), but it's not entirely clear what that would serve other than get the Doctor's attention.
But with all that said — "Mark of the Rani" is an entirely adequate introduction to the Rani as a character. Certainly better than "Time and the Rani" or (shudder!) "Dimensions in time"...!