In short, Tadoshi is basically used with "目的語{Mokutekigo}"-Object and "を{wo}" like "パン{Pan}を{wo}食べる{taberu}" - I eat a bread.
Of course, there is exception, but it is a rare case.
An exception case is as below.
猫が私の庭を走っている - Neko ga watashi no niwa wo hashitteiru
A cat is running in my yard.
In this sentence, "走っている" (infinitive verb is "走る{hashiru}) is Jidoshi because Niwa, yard is place.
In addition, if you can alternate "を{wo}" with "で{de}" like "庭{Niwa} で{de} 走る{hashiru}", it is not Tadoshi.
Your sentence,
A tadoushi verb acts upon another entity; a jidoushi verb does not.
I think this is basically correct.
However, in my opinion, some verbs like kiss someone or touch someone is Jidoshi. (Even in Japan, it is not clear.)
kiss someone is "にキスする{ni kisu suru}", and touch someone is "に触れる{ni fureru}"
This verbs act upon an entity/object, but are not paired with "を{wo}".
To make matters complicated, touch can be translated as either "を{wo}触る{sawaru}" or "に{ni}触れる{fureru}".
I guess the former is Tadoshi, and the latter is Jidoshi.
This is just my thought, but I understand that "触る{sawaru}" implies "touch tightly to check something or with a clear purpose.", but "触れる{fureru}" implies touch slightly or without his/her will.
So, I think this slight difference makes Japanese learner more confused.
I am not sure if kiss is Jidoshi or not, but if we follow the principle, kiss is Jidoshi because it is used with "に{ni}" (not "を{wo}").
Again, this case is gray and rare, but basically, Tadoshi acts upon an object and is used with "を{wo}"
In this case:
道を間違えたのかな (I wonder if I mistook the street)
道{michi}, street is object/entity.
道-を-間違えた {Michi-wo-machigaeta} is "I went the wrong way" (directly translated to" I mistook the street")
間違える itself, if it can indeed be translated as "to make a mistake"
I think "to make a mistake on something" is more correct.
Japanese often omit/skip object or subject.
A:コカコーラを買ってきてと頼んだのに、これはドクターペッパーだ!
B:ごめん。間違えた。(間違えた is the past tense of 間違える)
A:I asked you to buy coke by Coca-cola, but this is Dr. Pepper!!
B:I am sorry. I made a mistake.
In this case, B doesn't say what he/she mistook because it is obvious.
Correctly speaking,
B:ごめん。(ドクターペッパーをコカ・コーラと)間違えた。
B:I am sorry. I bought Dr pepper by mistake for Coca-cola.
By the way, In Engslih class in Japan, we Japanese learn that a verb which needs preposition is Jidoshi.
For example, "I go to school." It is Jidoshi because of to.
"I opened the door" It is Tadoshi because of NO preposition.
In this method, kiss or touch is an exception case. This is Jidoshi although they do NOT need preposition.
However, this is gray even in Japan. Some dictionaries say this is Tadoshi.
I think this is a rare case.
Does this answer your question?
feel free to tell me if you have qustions.