Plot hole: Enola and Tewkesbury make an unpremeditated decision to visit the Basilwether estate. This decision was made on the spur of the moment, and no-one knew about it. but when they arrive, Linthorn, who is supposed to be in London looking for Tewkesbury, is waiting in ambush to kill them. (01:32:45 - 01:34:31)
Suggested correction: Linthorn saw them in London. He travelled back to the Basilweather estate, and waited for them to slowly make their way there.
Enola and the young Tewkesbury were in London two weeks prior to Enola's forced enrollment in a boarding school where she was supposed to spend her next few years! Furthermore, there is no evidence of Linthorn having seen them.
Factual error: Linthorn meets his end when Enola knocks him off his feet. He hits his temple against a heavy and sharp furniture protrusion. Death must have been instantaneous, but instead, he lives to speak a few words. (01:39:18 - 01:39:55)
Suggested correction: He suffered a serious injury, but didn't die right away. There's no indication death was instantaneous.
Every word of what you said is correct. And that's the mistake! Death must have been instantaneous... that is if there was any. A "head trauma", as medical doctors call it, does not have slow-timed effect. The effects range from dizziness to more severe ones, e.g. loss of consciousness, loss of memory, or death. All of them are instantaneous.
Plot hole: No sooner than the film begins, Mycroft becomes the legal guardian of Enola; Sherlock accepts it without question. How on Earth did that happen? No coroner would grant a transference of guardianship just because someone's mother stepped out of the house and didn't return for a day or two. (00:11:37)
Suggested correction: The brothers obviously think that Enola's mother is out of her mind; Being the elder brother, Mycroft would immediately have had to take responsibility over Enola. Even if the mother did only go away for a day or two, Enola would still have required a guardian.
The brothers might as well think whatever they want. The UK's laws still mandate an inquest and a coroner's decision.