Some of you guys seem to be a bit paranoid and over the top. There are two different questions here and you're blurring the lines. The first question to answer for yourself is:
Is this the instrument I am looking for?
That's where this thread looked like it was directed. The second question is:
Is this a legitimate listing?
Is a completely different issue.
As far as the original question is concerned, here's what I think matters:
Simply, you need to know if the features you are looking for are there. Some players looking for their first Alembic don't need any info at all. They don't care if the $1200 bass is a Spoiler or Persuader, they just want an Alembic. This is a little bit foolish to me, but it happens.
Of course, when you're looking at $2K+ instruments, the bar is a little higher. Generally, an educated eye can tell almost everything about a newer instrument from looking at a set of photos. The older finishes and time aging the woods can trick you on the wood recipe. It can be hard to distinguish purpleheart neck stringers from walnut in a photo of a 20+ year old instrument with yellowed finish. Replacing the guts to change the tone was popular in the 80s and 90s as well. Since, in my opinion, the pickups and electronics are what sets Alembic apart from the best of the rest, knowing you're getting the original stuff is critical.
Beyond that, it's a question of what features matter to you individually. Do you care what woods were used? The scale length? The electronics package? If so, then ask if it isn't listed. For any Series instrument from before 2000 or so, I am concerned about the electronics upgrade since that can be a $1500 fix if it is needed.
The serial number is always nice if you can get it, but not critical to the decision. If it's a public for sale listing, a serial number check may not be done before someone else buys the item. You can, and should, check the stolen instrument listing though.
Now comes the hard part. You're looking at a listing for an '84 Spoiler on eBay with a buy now price of $2K. How long before someone else grabs it? Do you ask ten questions to see it sold before they are answered, or do you just do it? Your call. I might do it and ask the questions before paying if everything looks legit, or send the payment via PayPal and credit card so that I am fully protected. An old adage says that missing out is no big deal because there will be another listing in the future. Sometimes, especially for unusual pieces, it isn't really true.
Finally, let's remember that not every Alembic owner knows what they have. We've seen plenty of legitimate listings described incorrectly in every way. Woods are often mis-identified, as are electronics. We've even seen some set necks made to look neck-through and advertised as such. You can get a completely honest answer to any question you ask, but it may not be correct. Be prepared.