Stating the obvious, one has to do their homework very well. My first syndicate membership was based on the personal recommendation of a friend whom I trusted (and was a member of) and it largely worked. There are some bumps and disagreements on the way, and while this was a relaxed syndicate in terms of stated rules, the one rule that did matter was that whenever there was contention, there was a simple vote - majority wins (although it was a syndicate of 8 and in the 4 years I was a member, we only had two votes, both won or lost by a clear majority).
I sold my share 2 years ago and haven't found another suitable syndicate closer to home since. Some things to beware of - onerous conditions of selling your share, onerous restrictions on booking, ensuring there is sufficient funds in the account or that the other members are solvent and can afford cash calls, is there a designated administrator and/or maintenance coordinator - much easier, that there is a vetting procedure available to all existing syndicate members when taking on new members, that there is a protocol for deciding contentious issues, that there isn't any member that is in arrears and that payments are made promptly, the serviceability of the aircraft and its history (and the willingness of the syndicate to show you/walk you through the maintenance history - has their been recurring problems, is there a large number of inop instruments/aviaionics, etc); does the tech log look like there are cowboys in the syndicate; what are the shared responsibilities (keeping it clean, flying to maintenance base if not at home base, etc); if you want a bit of a social life within the syndicate, are their members who often fly with other members, etc.
Taking Old Koreelah's point, probably best to stick to Cert of Airworthiness aircraft because they are a lot less flexible with what owners can do to them.
(BTW, not sure in Aus, but in the UK, they syndicate can be forced to wind up and sell the plane if one member (of legally up to 20) decides they want out and a buyer can't be found - there was a collective sigh of relief when I purchased my share as I believe that is what the seller was threatening - thankfully it didn't could my friend's judgement).