In many things I read question marks are used after what is obviously a
question, but sometimes they are not used (even though it is the same person
who wrote it).

Is there a reason why, even stuff written by the same person, can be so
inconsistent with regards to questions having question marks?
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orthography
Is there a reason why some questions have question marks and other don't?
I would say that if the "ka" is used, then a question mark is unnecessary,
unless it is used as a courtesy to foreigners reading it. One user may forget
to use it sometimes because they are not used to using it at all in their
native language. What source are you looking at for someone using/not using
it? It might help slightly with a better answer.
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As I see it, it is mainly linked to the speech politeness that is used. In
informal speech, the question form is achieved by intonation mainly (and
often, some additional particles at the end), so in writing the question mark
is necessary. In formal speech, question particle is mandatory, so question
mark is redundant (and thus, not used):

ex. informal: 食べる。"Taberu." (I) will eat. 食べる？ "Taberu?" Will you eat? (the
subject is often ambiguous in Japanese, because it is not mandatory to include
it) or "Taberu no?" Will you eat?"

versus formal: 食べます。"Tabemasu." I will eat. 食べますか。"Tabemasuka." Will you eat?
The "ka" particle indicates, that is is a question - the question mark is
unnecessary here.

Or maybe you have some real-world examples, that one about you wrote? If so,
please post it, and I will try to better grasp the case and explain it
further.
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I agree with Ronk's answer. Many people are just not conscious of orthographic
inconsistency.

From a point of view of oral reading, question marks often indicate a strong
accent on the last character of the sentence to emphasize it's a question
(even if without using か) as seen in other languages as well.

> [これですか？]{LHLLH}
>
> [これですか。]{LHLLL}
>
> [どれにする？]{HLLLH}

In old novels, there might be a question without question mark nor か, like

> [どれにする。]{HLLLL}
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It can't be explained in terms of a single factor.

  * **Historical change of language**  
Interestingly, the question mark (along with exclamation) isn't defined in
Japanese orthography. Traditional Japanese language always has a question
particle or a question word in an interrogative sentence, which makes question
mark unnecessary. However, as modern spoken language comes to substitute
rising intonation for question particle more and more, explicit question mark
is needed more and more to avoid misunderstanding. For this reason, recent
writers use the symbol more than old-time writers.

  * **Writers' styles**  
Of course, it isn't that simple as every writer in a generation uses question
marks uniformly. Some of them use them in very conservatively, while others do
near-obligatory, even for similar content. Maybe you find great inconsistency
among writers, but think it as their writing styles.

  * **The meaning of the sign**  
The question mark is a punctuation, but as its introduction to Japanese as
replacement for question particles, more and more people have gotten to
understand this symbol as a phonogram -- that directly transcribes rising
intonation itself. If the writer maintains this stance, you can no more expect
the symbol to be indication of question; they don't put it in question where
the rising pitch is absent or weak (such as in rhetorical question), but
attach it when the rising appears outside question (such as in
[uptalk](https://en.wikipedia.org/wiki/High_rising_terminal)?).
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