Where can I find out if there was a firmware update?

We don't have release notes for minor updates.  Typically, if you see something with a third digit that's non-zero, it is a branch specifically to support hardware that wasn't ready when the main branch was made -- for example, 8.1.0 was a major OS release, but 8.1.2 was made to support the a number of Roku TV models that were released while 8.1.0 was being finalized.  The minor branch is made to avoid destabilizing the builds used for most of the Roku devices with changes for those specific models.

If it's just a build number change, like 8.1.0.4102 to 8.1.0.4143, that's usually just a bug fix, addressing some issue seen during beta testing or during the staged roll out.

Thank you for the explanation. 

So we started channel development a little bit ago I think on firmware 8.0 and then 8.1 came out. 8.0 supported something we were doing with subtitles and 8.1 does not. That is all fine, we hadn't released the channel yet. But that got me worried that things will change like that in the future and users will get upset, so how can I get preview releases for Roku, like I do with Chromecast for example? 

The beta program is how we do early releases.  Details on joining are at https://forums.roku.com/viewtopic.php?f=34&t=112555

Ok, I had already applied there. How long does it take to go through the application process? It has been at least a week or more.  

Just got approved for the beta, thanks.