Ryan,
I am a mortgage broker and I've learned a lot about this in the last few months. I have a borrower who owns a investment property in the US Virgin Islands. He holds every single property he owns in a separate LLC for tax/legal/liability issues, and he's a Harvard CPA.
However, this presents MANY problems when you try and refinance or purchase. Nearly every mortgage loan is sold on the secondary market. So Lender A will fund your mortgage loan and then sell it to large institutional investors. Well these investors will not purchase loans that close in the name of an LLC, which is why nearly every lender can't do it.
To get a mortgage that will close in an LLC, you have to find a "Portfolio Investor/Lender". These are lenders who DO NOT sell their mortgages on the secondary market. These lenders are typically banks.
In my borrower's case, he's going to close in his name and then transfer back into the LLC. Now technically, if the lender found out he did that they could call the loan due. But they obviously won't find out as long as he's making his payments. The kicker is the transfer taxes. Since he's transfering ownership from the LLC to himself, he's subject to the tax from the county/territory.
So while there are many benefits to keeping it in the LLC, when it comes to refinancing it can be a real hassle.
Hope that helps...