What do you look at most closely when you are thinking about taking on another team? How do you evaluate it? What particular things influence your decision to call or fold the most? 

I really don't care as much about the shape of the team as much as I do the shape of the league. So turnover and parity matter.

Has to be a private league and one that does not go public every time they roll because they won't wait for owners.

I look at the league rules, if there are not any I probably am not joining. I really wish every classified thread contained the league rule

I am also a sucker for "we are trying to make the world better and here are the rules we put in place" threads.

1) Quality of teams available, History of trades, draft picks and IFA's that the team I'm interested has signed in recent years.
2) How much overall money is poured into IFA each season.. If I see a 40M or less payroll team that is consistently winning and signing the best IFA every season. I will likely move on.. 
3) Almanac to see if the same teams are winning every season..
4) If the world is consistently doing owner swaps to fill each season I will usually pass.

I was looking to maybe add a team in the next few weeks and I noticed that there are a lot of dogcrap worlds and teams out there..

Owners that are currently in the world.

I have to agree with crickett13 about the private league going public just to fill and roll.  I've had a couple of bad experiences with that already in my limited experience.  I joined thinking it was an open world and started getting warnings about win minimums within the first 50 games.  I'm like, "Wait a minute, this was an open world when I joined."  I've seen several new owners get roped into a world like that and while they're trying to learn the game, get constantly harassed and threatened before they even get started.  Some of them quit immediately and never return.  It really is unfair for private worlds to go public and HBD as a whole is suffering for it.  Now when I select a world, if they were private and have 10-15 openings and went public to fill, I avoid them altogether because if almost half the world bolted, something is wrong.

The problem with private worlds going public is they can't enforce their rules so that's nonsense that they pull that.  If they want to have a private world with their own rules that's fine up until they decide they can't wait to fill and go public, then they should just shut up. 

I want to know who the commish is and if they have rules against tanking.  A world needs a strong commish to keep things from getting out of hand with 32 competitive people fighting for the same title.  As for a team I want either some talent in the majors or minors so there is something to work with.

The world was Morgan.  They started the season public with a 50 win minimum and tried to enforce it.  Halfway through the season, the commish added a rule limiting prospect budget to 50% of player payroll.  So if your player payroll was 50m, your prospect budget couldn't exceed 25m.  He did this own his own without a vote from the other owners.  I submitted a ticket to WIS to get clarification on the rules and they stated, clearly, that if a season is started "PUBLIC", then standard rules apply and "PRIVATE" world rules can only be enforced if EVERY new owner agrees to it.  Needless to say, I exited after 1 season.  Was accused of tanking even though my player payroll was 95m.  I just had a really expensive "bad" team.  Under constant pressure, making many moves until I ran out of money, finished the season 55-107, my worst season EVER.  If this had been my first world, trying to learn the game, I would have never returned to Dynasty at all!!  Anyway, paid $25 for 3 months of harassment and they ended the season with about a 50% owner exit.

Correction, only 12 owners left.