1801 will probably be need to be open for MSMQ, I think it depends on the exact version of all of the solarwinds components. Nothing fails exactly, you will just get odd errors.
On some versions this is used to communicate to the remote poller force rediscovery, polling, list resources on nodes, and without it being open they fail with some odd error.
On other versions they reverted to using the 17777 business layer port for this function.
this is/was broken when you have FOE installed, since they bound to the specific IP address of the additional poller, not its name, so when you are failed-over the messages don't go anywhere useful..
port 80 is not needed -- the only purpose is for when you run the installer to the 'open web console' link works after the additional poller is installed.
port 17778 is only needed to communicate with the SWIS engine, normally running on the application server; the Additional poller does not use this. (this might have changed after 10.6, but I've not tested that)