"Because, that still doesn’t fix peoples' reading problem."
I heart irony.
I hope you love irony enough that your entire post was ironic, otherwise you simply attempted to correct a sentence that needed no correction, and got it wrong.
People denotes more than person. The possessive of people is people's
Peoples is the plural of people and therefore denotes multiple groups of people. The possessive of peoples is peoples'
Ordinarily you would use peoples when you are talking about people of different communities, groups or race or type. You use people to discuss more than one person of the same community, group or type.
Here he has a single group, people with a reading problem, so it should have been classed as people not peoples.
Also the comma after because is superfluous. Whilst stylistically some people would add it, it is not required.