As one of her 'friends' reminds her at Tanya's wedding, she's never even had a boyfriend...
I don't think Muriel had any type of intrinsic mental illness per se, save for a lifetime of being emotionally and verbally abused by her domineering father, who was, at every turn, calling Muriel "useless." He compounds this by humiliating her publicly and specifically:
— She comes out, she can't even type.
I could type.
— Then I get her a job at me solicitor's. After a month, Stevie Mason rings up and says he'll have to let her go... 'cause she can't type.
If I couldn't type, why did they give me my secretarial diploma?
— Because I paid for it!
— Sits around the house like a dead weight...
— watching TV, sleeping all day, getting arrested at weddings!
— You're useless.
— You're all useless.
— A bunch of useless no-hopers.
Her outburst in the bridal shoppe is a direct result of his neglect/abusive words:
Muriel! Muriel Heslop! Stupid, fat and useless! I hate her! I'm not going back to being her again!
Bill Heslop's spirit broke her Mum's, pushing her fragile hand (from whence I think Muriel received her childlike innocence) into committing suicide. The time away from Porpoise Spit was enough for her to get her bottle and face him:
You owe us, Dad. We're not useless. We never were. Now you're looking after the kids...and you're gonna tell them they're not useless.
A lifetime of insufficient socialisation, combined with daily reminders of how "useless" they all were, produced this broken household, mother worn down and children who have no idea how to function in the world outside of the inhibited universe in which they'd been all of their lives.
Although I don't think she is mentally ill, I do think the "mental things" that did, in fact, happen to her took their toll... and will be slowly undone, the more distance she puts between her and Porpoise Spit, which is the "Happily Ever After" ending of the film.