The latest version of the Play Store is no longer 3.7.11 - say hello to v3.7.13. I haven't found anything different from 3.7.11 just yet - it likely only contains bug fixes. There's no reason to lag behind, however, so if you're running a Play Store with a version lower than 3.7.13, jump right to the download mirrors below. Before you do that, let me point out a few things.
Upon playing with the Store further, I did discover a new feature compared to v3.5.19 that I didn't mention last time - inline app links in search suggestions. Take a look at searching in 3.5.19 (on the left) and 3.7.13 (on the right) - direct app links are now mixed in with suggested spellings. A subtle change, but if I can save a few clicks here and there and get to results faster, why not?
And a few earlier ones:
If you missed the 3.7.11 post, I'll mention this feature again as well - you can now set your preferred sharing method (long-press on the new field to the right of the share dropdown). I set mine to Gmail so that I can quickly share new apps with the team. Neat.
The APK is signed by Google and upgrades your existing Play Store. The cryptographic signature guarantees that the file is safe to install and was not tampered with in any way. Rather than wait for Google to push this download to your devices, which can take weeks, download and install it just like any other APK and enjoy the new Play Store experience.