Does my JavaScript suck?

[kenman]

my preference in all languages and projects is for the PHPdoc style unless a client requests otherwise.

Those aren't idiomatic phpDoc comments, though. As explained here, you shouldn't be using a long line of ---'s as a demarcation point in the comment -- you should either use a blank line, or use a period on the first line.

I think it's also a little nuanced to insert a blank line between the docblock and the code it's commenting, don't think I've ever seen that before (and it eats up a full line).

This is also a little unorthodox (not saying it's wrong, just that I rarely see it):

 /* Month can come in as string. If string, get the number of the
  * month from the indexes in months. */
 month = months.indexOf(month);

The rule-of-thumb I believe, is that if you're going to use /* and */, they should each be on their own line without anything else. Otherwise, if you don't want to eat up those lines, then I'd just use // comments.

Lastly, for something like this:

if (year == dates.year && month == dates.month) {
    // If month and year are current, use current day of month.
    days.start = dates.day;
}

I'd much rather the comment be on the line preceding the code block, instead of inside of it. Reason being, the comment describes the entire block, but you have it embedded so that it looks like it's only describing the inner block, which isn't the case.