What more can be done to better improve my ThinkPad T420?

The drive caddy and covers are still available. I would put an SSD in there and max out the RAM if it's not already.

In addition to what others have suggested,

• If it didn't come with one, a 1600x900 display and the corresponding cable (it is different from the 1366x768 cable). It may be cheaper to harvest a busted unit with said parts still intact. If the seller photographed a sticker with something like "TYPE: 4177-28S", you can look up the resolution of the screen it came with on tp.krelay.de. The LCD options do max out with 1600x900 TN panels. No 1920x1080 or IPS options are available, barring exotic converters like Nitrocaster and a.gain.
• Ram is upgradable to 16 GB. 16 GB on a single DDR3 SO-DIMM exists, but the memory controller isn't compatible with those.
• Flashing coreboot will let you use Ivy Bridge CPUs. This does require disassembly and a hardware chip programmer like the CH341a. I'm happy to elaborate on this since I've installed coreboot on every supported ThinkPad in my possession. Coreboot also has no wireless card whitelist.
• Between dual-core options, the performance from i5 to i7 only increases marginally. But if you choose to flash coreboot, you can upgrade to the quad core i7-3632QM, which gives much better performance within the same 35 watt limit.
• Replacing the CD drive with a SATA hard drive caddy, if you don't use optical media much.
• KingSener battery. Highest capacity batteries I've encountered thus far. The 40 USD "Genuine" batteries with the "RECYCLE 1.800.822.8837" emblem in wide font are a close second. There are genuine old stock batteries, but whether they work after being stored for so long is anyone's guess.
• USB 3.0 ports via ExpressCard, caveat being the non-negligible idle power draw of the card.