I'm trying very hard to get you the 38.0.1 beta by sometime next week, probably over the July 4th weekend assuming the local pyros don't burn my house down with errant illegal fireworks, but I keep hitting showstoppers while trying to dogfood it. First it was fonts and then it was Unicode input, and then the newtab crap got unstuck again, and then the G5 build worked but the 7450 build didn't, and then, and then, and then. I'm still working on the last couple of these major bugs and then I've got some additional systems to test on before I introduce them to you. There are a couple minor bugs that I won't fix before the beta because we need enough time for the localizers to do their jobs, and MP3 support is present but is still not finished, but there will be a second beta that should address most of these problems prior to our launch with 38.0.2. Be warned of two changes right away: no more tiles in the new tab page (I never liked them anyway, but they require Electrolysis now, so that's a no-no), and Check for Updates is now moved to the Help menu, congruent with regular Firefox, since keeping it in its old location now requires substantial extra code that is no longer worth it. If you can't deal with these changes, I will hurt you very slowly.
Features that did not make the cut: Firefox Hello and Pocket, and the Cisco H.264 integration. Hello and Pocket are not in the ESR, and I wouldn't support them anyway; Hello needs WebRTC, which we still don't really support, and you can count me in with the people who don't like a major built-in browser component depending exclusively on a third-party service (Pocket). As for the Cisco integration, there will never be a build of those components for Tiger PowerPC, so there. Features that did make the cut, though, are pdf.js and Reader View. Although PDF viewing is obviously pokier compared to Preview.app, it's still very convenient, generally works well enough now that we have IonPower backing it, and is much safer. However, Reader View on the other hand works very well on our old systems. You'll really like it especially on a G3 because it cuts out a lot of junk.
After that there are two toys you'll get to play with before 38.0.2 since I hope to introduce them widely with the 38 launch. More on that after the beta, but I'll whet your appetite a little: although the MacTubes Enabler is now officially retired, since as expected the MacTubes maintainer has thrown in the towel, thanks to these projects the MTE has not one but two potential successors, and one of them has other potential applications. (The QuickTime Enabler soldiers on, of course.)
Last but not least, I have decided to move the issues list and the wiki from Google Code to Github, and leave downloads with SourceForge. That transition will occur sometime late July before Google Code goes read-only on August 24th. (Classilla has already done this invisibly but I need to work on a stele so that 9.3.4 will be able to use Github effectively.) In the meantime, I have already publicly called Google a bunch of meaniepants and poopieheads for their shameful handling of what used to be a great service, so my work here is done.