These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Even lampshaded a bit in-movie, both by Daniel himself ("What am I doing here? This is beyond obsession.") and by the judge, once the gig is up, as the reason for ordering supervision during Daniel's time with the kids.
In some ways, this also applies to Miranda. Is she a mature woman who has put up with Daniel's antics over the years and has finally reached her breaking point, or is she a cold detached woman more interested in her career than her family? Her apparent mooning over her old flame prior to telling Daniel it's over doesn't help her cause any.
Indeed, leading to wondering over the interpretation of whether she's sincerely at the end of her rope with a situation that's bad for her and her children, or just looking for an excuse to dump her current husband for her more attractive, more successful, and less silly ex?
Designated Villain: Stu is an exceptionally caring and polite individual to Miranda and the kids, so much so that Daniel sabotaging their relationship can come off as unnecessarily spiteful.
This is likely intentional and Stu is not intended to be a villainous character per se, see Romantic False Lead on the main page.
Daniel says he can't live without his kids, just like he can't live without air. Robin Williams committed suicide by hanging himself.
Early on in the movie, there are scenes of Daniel struggling with depression and denial. These moments became a lot tougher to watch after Robin Williams was Driven to Suicide by a struggle with depression.
Heartwarming In Hindsight: After Robin Williams' death, Mara Wilson paraphrased her most famous line from the film, saying of all the younger people who either worked with him or were fans "We're all his goddamn kids too."
Tear Jerker: Two specific moments in the movie: Daniel's speech to the judge explaining why he dressed up as Mrs. Doubtfire, only to have the judge impose harsher limits on his visitation rights, and Daniel's/Mrs. Doubtfire's response to a letter from a child whose parents are separating... which serves as background narration for the Bittersweet Ending in which Miranda revokes said limits.