For me, the number one problem of Google+ was that many who were excited to try it, couldn't (for over a year, if I recall?). We were a 2nd-class-citizens with a Google Apps account, rather than a Gmail account.
You say that like it's a short amount of time. Three months is more than enough time for hype to build, peek, and wither, which can -- and did, I would agrue -- kill a social network.
I don't disagree; I think that slow rollouts of large products make sense from a technical standpoint (you can make sure that nothing breaks down at the large scale, and fix problems before they become a big issue), but I think that invite-only betas which last weeks or months can often hurt product uptake.
I was just clarifying that the invite-only stage didn't last more than a year.
A slow and phased community development worked really, really well for Facebook. Remember: it was deployed into a world already dominated by MySpace and with multiple rivals.
Slower, with a solid core community, would have been far better for G+ IMO. It opened up too fast.
Not only didn't it have a gelled community, but there were far too many UI / feature glitches and omissions. Many of which persist to this day.
But Facebook had a rather ingenious strategy for their slow rollout. They rolled out an entire college at the same time, so once Facebook was available for you, it was also available to a significant part of your friend group (the lifeblood of a social network). Google+ however just released slowly to a random set of people, so some people could get on, but none of their friends were there.
sjs383 is referring to google not allowing/enabling accounts on "Google apps for your domain" domains (vanity or business google accounts, essentially) to get on plus.