There are a few performance issues that you may experience. For example, if you're into online gaming then your latency will likely increase. Your internet connection bandwidth could also be limited by either Mullvad's servers, your router, or any of the additional hops necessary due to the VPN. There's also the situation where you have no internet connection at all due to an issue with the VPN connection.

There are also some user experience issues that users on the network nay experience. For example, any location based services based on IP address will either not work at all or require manual updates by the user. The same is true for other settings like locale, but they are hopefully better handled via browser/system settings. What's more likely is content restrictions due to geographic IP addresses. Additionally, some accounts/activity could be flagged as suspicious, suspended, or blocked/deleted if you change servers too frequently.

I'm sure you are either aware of or thought through most of that, but you may want to make sure everyone on the network is fine with that too.

In terms of privacy and security, it really comes down to your threat model. For example, if you're logged into Facebook, Google, etc. 24/7, use Chrome, Windows, etc., and never change the outbound Mullvad server, you're not doing too much more than removing your ISP's ability to log your activity (and maybe that's all you want/need).