I think uniqueness is 特質、個性、持ち味、or something like that.
From given phrase, I am not sure if the last いて is needed, and if 'one' is 自分 or 人, but I guess you're right, and other than that, it's just perfect to me.
Ｉt's grammatically correct.
I humbly suggest you that you can use 弱味, too. 弱さ is really okay, and actually some may use 弱さ in this case. 弱さ is weakness yes, whichever physically or mentally, but 弱味 means the property, characteristic of weakness, so it can include 'disadvantage' at the same time.
I think 特点 is weird.
I think 特長 （not 特徴 here) is maybe the most proper translation in this context.
I don't think 弱さ is weird.
Maybe some people don't like to use 特長 here, because it might be saying too much of the weakness.
In that case, 特徴 is the candidate to choose.
I think I found a better translation:
If the subject person thinks that the uniqueness is their merit, 個性的な特長 is the best translation, I think.
If the subject person thinks that it is just a uniqueness, and not their merit, 個性的な特徴 might be better translation.
Without more context, I somehow feel 特長 is better in this context:"Considering even one's weaknesses as uniqueness, [...]" because of the word "even."
"Considering one's weakness as a merit of uniqueness, ..." "Considering one's weakness as uniqueness, affirmatively, ..."
If the subject person or writer doesn't think that it is a merit at all, then "自分の弱ささえ個性とみなしていて" is better and concise.