Welcome to Facebook, Sheryl Sandberg! Use Your Google Search DNA, Pretty Please.

Now in her second week at Facebook, new COO Sheryl Sandberg (pictured here) probably thought BoomTown was done making suggestions of things she needed to work on at the social networking site.

Not even close! (Although we promise eventually to do a post on things BoomTown likes about Facebook.)

But that day is not today, where the focus is on search. It is a topic you should know a lot about, given those half-dozen years you spent at the Googleplex as one of its top execs.

And while your job focus was on ad operations, one cannot imagine you did not pick up a thing or two about search, which is like oxygen there.

And, I am sorry to say, if this was the case at Facebook, we would all be turning a magnificent shade of blue right about now from lack thereof.

That’s because search on Facebook, which is billed as a place to find friends, is about as bad as it can be. In fact, it has so few features and so little usability that I would be better off tagging some of my friends with those dog-collar homing devices to keep track of them.

Case in point is my email (which I have already whined about here). Last night, I was searching for a particular email from the fall and had to slog through page after page of unorganizable emails to find it purely from memory.

And your new feature to make lists of friends is very time-intensive, even though it is described as: “Now you can easily organize your friends into convenient lists for messaging, invites, and more.”

But it is a lot harder than it seems, with only snapshots and names to use as you are selecting how to organize them.

Currently, for example, I have 661 friends I made before being able to even make lists, with 217 more requests I am ignoring, since the prospect of a massive list I cannot manage is exhausting, even though I know there are people in there I want to interact with and know about without opening up each and every profile.

While it is nice to now be able to add friends to a list, it is still much too crude a way to understand this important social graph.

So instead of being this enlightened ecosystem, my friends list feels like a really good library with all the books scattered on the floor in a messy pile.

That makes things hard, since some friends are real friends and some are people I kind of know and others people who like BoomTown, for example.

It would be nice then to just have a way to drag and drop these names or present me with some more sophisticated way search and sort them.

The same search problems are present all over Facebook, where almost nothing is searchable in an easy way.

I did a universal search, for example, of Barry Manilow–your god of music and mine (Vegas, baby!)–and got 424 mostly meaningless results (as you can see below; click on the image to make it bigger).

And don’t even get me started on trying to search for good widgets–but let’s just say it makes the quest for the Holy Grail look simple.

Thus, I have a very good suggestion with what, what, what you can do with yet another slug of money–$60 million more–that Facebook got recently from Hong Kong tycoon Li Ka-shing.

No, not a set of those pricey Japanese massage chairs or automated toilets seats that blanket the Google (GOOG) campus from whence you came. No, not MacBook Airs for all at the startup. No, not even a lifetime supply of Red Bull for the gang-that-likes-to-work-all-night in Palo Alto.

Right now, you have $120 million from Li, to go with the $240 million Microsoft handed over, and I am guessing Facebook breaks even on operations, so you might still have some errants tens of millions left over from earlier investments.

This is a lot of scratch to work with to create a world-class search to make Facebook what your CEO and Founder Mark Zuckerberg calls a “utility.”

And utility means useful, so get busy on creating a search product worthy of the well-organized profile pages that Facebook is known for.

That, or fork over some dough for Google or Yahoo (YHOO) or Microsoft (MSFT) to do it for you.

Please see this disclosure related to me and Google.