With regard to anti-spam practices, what exactly does a typical reverse DNS check look for

The test isn't normally comparing against the SMTP envelope (like you describe as your eyeball-based process), but finding the reverse DNS hostname of the connecting host (if any), running that through forward DNS and seeing if it resolved back to the original IP number.

So what you need is 1) to have reverse DNS set up (for the first step) and 2) to have it set up correctly (for the second step).

There's nothing to stop anyone from comparing with the SMTP envelope as well, even if that's frequently seen as too paranoid, so you'd also want anyplace your hostname appears in your mail transmission to use the DNS name that appears in your reverse DNS.

Note: There's some opinionated ranting in this. You're free to ignore it :)

Ok, this is email we're talking about, so we should start by saying there is simply no way to guarantee deliverability of a message. SMTP was devised in a quieter, more trusting time. Since then, many people have implemented what they see as the final solution to spam, only to be amazed that it hasn't worked; or that the spammers have figured out how to defeat it; or that it relies on everyone having done it to be effective. (or dozens of other reasons). What we have now is mess of balkanized systems and half-implemented ideas that mean that it's practically impossible to ensure your message will get through.

My opinion is that most of the best practice should be centred around receiving email, rather than sending it. As as sender, it's not your job to ensure it meets whatever random measures the recipient has in place. It's their job to ensure their filtering doesn't block legitimate mail based on assumptions about what a mail message should look like; many of which don't take full account of the interesting ways in which mail can be routed and delivered.

First, what I can't find anywhere is whether or not the domain name of the From: email address needs to match the domain name of the SMTP server.

In principal, no. There are many legitimate reasons why an MTA will send mail from addresses that have nothing to do with its own domain. You might come across systems that reject your mail for this reason, but this is not your problem. It doesn't hurt to have your PTR records match your domain and for the HELO announcement to match those, at least at the TLD; but anything that rejects purely because the From: domain doesn't match the PTR TLD is broken.

If so, then I am confused by the advice given here, specifically (in a listing of bad case scenarios):

No SPF record for the domain being used in the HELO command.

SPF records are another of these "it sounds right in principal" ideas (See here for another rant on that subject) that has gained a lot of weight. The main problem for me is that a lot of MTAs unfairly punish domains that simply don't publish any SPF at all. Again, this is not your problem.

That said, I've put one in place for our domains, because it's not done to get mardy with customer sysadmins too frequently. It ends up being a political decision, rather than a technical one.

If you're going to use SPF and leave your PTR and HELO as abc.def.linode.com; then the SPF record for all of your From: domains should list that server as a sender. If you don't have control over foo.com and bar.com DNS, then you'll have to talk to someone who does.

I'm currently using the linode.com SMTP+PTR domain and example.com From: address combination without much of any deliverability issue

and neither should you have. If you publish SPF at all and the linode.com seerver isn't listed, then you'll get bounced a lot. However, if you have listed it, or if example.com doesn't publish any SPF records at all, then you should be fine. (I repeat my earlier point that MTAs rejecting mail because there's no SPF published at all are broken and probably bouncing a lot of legitimate mail).