I agree that all necessary information, including dress code if there is one (see below), ought to be on the invitation.
Not registry, directions, hotel info, etc. Send that another way or include a note referring guests to the web site. Particularly not registry info; I get it that many people appreciate the convenience, but many others are put off by it, and you don't want your invitations to have that effect even on a few. The idea is that you don't want to be connecting your wanting people to share your wedding with the idea that they will give you gifts (and that you are eager to direct what those gifts should be).
If hosts/HCs don't want a specific level of dress, such as black tie, and the venue, time, and style of invitation give enough indication, then fine, although they will still get inquiries. But if they want black tie or cocktail attire, or beach or boat attire, or anything other than just a nice day/evening outfit, they need to put it on the invitation (or reception card, if there is one).
A wedding web site is not a requirement even to have, let alone for guests to check. Do not ever assume that all your guests are going to consult it, unless you specifically tell them they need to, and maybe not even then. People put the invitation up on the bulletin board or fridge and then forget that they were directed to additional information elsewhere even if they did hear you the first time.