Looking at the latest set of comments in this thread from a few months ago it seems like the problems I noticed when playing Venice are the same ones others have noticed for a while. Specifically:
1) a lack of gold due to the nature of puppet gold generation/costs (which seems especially weird given Venice's 2x trade routes)
2) a lack of supply, again due to puppets not generating enough supply
In my specific game I went to an extreme and puppeted 10CSs pretty quickly (only 5 were from normal MoV births, the rest were from an early adoption of TTGOG, Leaning Tower, Artistry policy, and the free one at trading). These 10 CSs were actually pretty ideally placed for defense- 6 of them were on a subcontinent island where they could pool their defenses and the rest were clustered closely to Venice. I should say that I was going the "tourism" route for Venice with my choice of optional UB (tradition/artistry/rationalism/freedom).
However, from the get-go my supply cap was a serious issue. On average I could only have 2 units per city for a lot of the game and only 3 units per city later on (once most of my cities had castles/arsenals up). Obviously I concentrated my forces at strategic locations to maximize my defense but a unit cap of 22-33 or so makes even defensive warfare in a human's hands very difficult, especially when many CSs are coastal and a navy might be necessary. I managed to stave off a few serious invasions anyway, at least until the late game when I think my relatively low unit cap simply made the rest of the world see me as an easy DoW target regardless of the positive modifiers I had groomed.
The gold problem was very surprising to me given Venice's 2x trade routes. It seemed like even when I had all of my trade-routes up and running my GPT was never that high compared to the rest of the civs in the game. This is especially problematic for Venice when purchasing things in their puppets is their only real option. I pretty much never had the gold to invest in puppet buildings and had to save it all for unit upgrades or investments in Venice.
One other issue I saw is that when puppeted CSs with MoV the CS would lose a bunch of its buildings. I would puppet a CS only to see its city combat score drop to 9 and the first building it starts working on being a wall. Looking at the available buildings to the puppet I would see monuments, etc that it surely already had. I imagine this is a bug and I have reported it on github. The puppeted CSs having to slowly rebuild walls exacerbates the low supply cap issue- the units I gained from puppeting the CS would often put me over my supply cap as the newly acquired city wasn't giving me enough supply to handle them!
If I played Venice again I would probably not puppet quite as many CSs (I mostly did so this game due to finding that 6-CSs mini continent and seeing it as too good to pass up) and instead plant a bunch of my MoV for Colonia. Having fewer costly puppets and more Colonia would hopefully alleviate some of the gold problems. However, fewer puppets would mean less "free" science/culture and an even smaller unit cap which I imagine would cause more friction with the AI as they see me as weak. To alleviate this I would probably target as many supply-giving wonders as I could- Himeji, etc. It's not very intuitive to go after those as Venice if you're going for a tourism victory but it seems almost necessary. I actually tried to get Himeji in my game once I realized how low my unit cap was but got beat to it by just a few turns.
I know people have said in the past that Authority Venice is quite strong. In the very early game their unit cap is probably not too low so that's probably their only chance at conquering. However, I don't really see how anyone could reasonably conquer past the early game because no matter how many puppets you get your unit cap is just too low. Aside from that, Venice has very little in the way of military perks to make warfare easier- pretty much just the optional UB that has the combat flavor. If you're able to conquer as authority Venice it seems like you're overcoming some pretty big handicaps. I would be interested to see someone pull that off at Immortal/Deity after the last few months of AI combat improvements.
Also, in basically every game where a Venice AI is present he is pretty much always gone very early on. The AI doesn't have the benefit of a human strategic mind to have any hope of survival from what I've seen. An AI with low unit cap and a spread out empire is basically doomed.
In any case, based off of my game I would probably recommend:
1) fixing the issue where CSs gained via MoV lose buildings.
2) doing something with the supply cap. +1 cap from each MoV might be enough or adding supply to the UB might also be necessary. I think this is the biggest problem- having low unit supply invites the AI to gang up on Venice which has the add-on effect of often taking away all your sweet, sweet trade routes (aside from just outright killing Venice, of course)
3) possibly improving Venice's gold, though if the above two issues were addressed (and if someone uses MoV more responsibly than I did...) then perhaps this would be a non-issue.