Putting aside the specific issue of felons serving on juries.
A hypothetical issue with the concept of "a jury of our peers" could be defining "peers".
Are there situations where the issue being litigated is sufficiently specialized that the average person would not constitute a peer? For example, determining whether an engineer followed proper practices.
At least in America, is so little shared world view between different segments of society (Democrat and Republican, rural and urban, upper class and working poor, west coast and deep south, etc.) that a given pair of citizens might effectively not be peers?
These concerns could be especially important since the law often depends on determining what a "reasonable person" would do in a situation which might vary depending on the "reasonable person's" background.