I am considering to move dns hosting to Linode. I know there is some restriction on the ip address a.b.c.d in the records, but that using MX records for gmail is allowed.

Can I have a subdomain that I dynamically update with my home dynamic ip, using a shared key.
1. My ISP decides to change my ip to 1.2.3.4
2. My box at home detects the change and updates linode DNS manager with:
home.mydomain.com A 1.2.3.4
where 1.2.3.4 is a non-Linode IP address.

is that allowed and possible?

You can point your domain recoreds at whatever you want, as for the automation the linode api would be ideal for that http://www.linode.com/api/index.cfm/

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someone posted a shell script in here a while back for doing that via the api. I recently lost it and haven't done a search to find it yet.

edit: got unlazy!

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