For full context see here: https://www.docdroid.net/oraqSdS/img-20170830-0001-new.pdf
The sentence is from 21-22: 聖人君子か大うそつきか、または自分がエラーをしていることに気が付いていないか、忘れてしまっている一番困ったひとかもしれない。
First, I wouldn't have a problem with this sentence if the bold かもしれない was か+も+知れない, but since the kanji is lacking I guess it is just かもしれない indicating that the speaker feels very unsure about smthg..
I interprete the か after 大うそつきか etc. as the か marking an indirect question. Since there is no question word like なに どう etc I'd expect かどうか but there already was the case that かどうか wasn't used and instead just か has been applied (I asked about this here and I was told that it was perfectly normal that this could happen).
Now, here my translation: "It could be a perfect person or a big liar, or someone who doesn't notice the mistakes he makes himself, or a person who is troubled by forgetting (forgetfulness?) the most."
What's also confusing me is that 困ったひとかもしれない lacks another か between かもしれない and ひと. I'd say that 困った人 also belongs to this long chain of indirect questions. I've never learnt that the last part of such a chain could omit its か. But maybe I got it wrong in the first place, thats why Im asking ^^