OK, so here's the list of problems I've encountered, they can be reproduced by using (except non-EUI Vox Populi) the latest versions of JFD's, Steam release if available:
CiD
ExCE
RtP
CulDiv
EC
Other mods seem not to affect the bugs.
1. I cannot invest money in non-Vox Populi wonders, the cost shown is -1 gold and clicking the button has no effect, there's no problem with the buildings though.
2. This may be intentional, but Venetian Great Magistrates can annex cities instead of just decolonise them.
3. Pushing claims on City States is overpowered. AIs integrate them like mad, there's almost no way to get World Council votes as at the beginning of Industrial Era there are like 2 CS's left. Even CS-oriented civs like Portugal and Austria do that.
4. Some piety level texts in Religion panel are not displayed (TXT index shows instead).
5. Shackles are the only way of improving your relations with City States without spending Production as you purchase both diplomatic and military units with them. This leads to snowballing effect - allying militaristic CS and establishing a Trade Route with it provides more Shackles and units, which can both be spent on allying another militaristic CS. The one to ally a militaristic CS early on will likely ally all the CS's before any other civ manages to do so.
6. Is it intentional for all the cities to be plagued constantly? Throughout 6 games I haven't seen a single city with positive health output.