To me, Dear all conveys laziness. A well-thought-out message should have a specific audience that the message applies to. Dear coworkers, Dear minions, Dear Death-Eaters, Dear residents, etc. is not that much more difficult to type. Then someone reading the message can more easily discern whether the message applies to them or not.
It's neither a subject nor an object. When I was in school this was called a "noun of direct address". When I took Latin it was called the "vocative case". That is when you use a word to identify the person you are speaking to. The most common use is sentences like, "Bob, come here!", where you may need to identify whom you are addressing, e.g. in a crowded room. It is also used in cases where there is no ambiguity as, basically, just a polite insertion. People sometimes intersperse the name of the person they are talking to in a long string of statements. Like, "And then I went to the store. And you know, Bob, I think that ..."
Usually it is set off with a comma. Like if you say, "I forgot, Sally", you are telling Sally that you forgot some unspecified thing. But if you say "I forgot Sally", then you are telling an unspecified person that you forgot Sally. So we usually write "Good Morning, Jane" rather than "Good Morning Jane". That's more of a greeting than a salutation, i.e. it's a complete sentence. "Dear Jane" does not call for a comma because there is nothing to set the noun off from: "dear" is an adjective modifying "Jane", so both together make up a noun (phrase) of direct address.
I suppose you could add words to the sentence to turn it into the object of a verb, like say that "Good Morning, Jane" is an abbreviated version of "I hope that Jane has a good morning." But I think that's a little strained. You're completely restructuring the sentence.
(I see RegDwight uses the term "vocative" to refer to this usage in English. I'd never heard that before, but whatever, it's the same idea.)
Best Answer
I never put old-timey snail-mail salutations on emails.
That being said, for the first email you send to someone you don't know, yes you should have a short sentence at the top explaining who you are and/or why you picked them (of all people) to contact. (eg: "I'm having a bit of trouble with product-X, and the website suggested I send a request to this address"). This is the same kind of stuff you'd start out saying if you'd phoned, after the obligatory "hello","hi" verbal handshake that we don't do in emails.
This is done because most folks these days get a lot of email of all kinds, and thus have their finger poised over the delete button on any email from a sender they don't recognize. As a courtesy to them, you should give them all the information as soon as possible to make their decision on whether to keep your email, direct it to someone else, or (horrors!) trash it.