I've used several of the LCDs from sparkfun that have backlights with both the regular arduinio and arduino mini.
It took me a (way too) long of time to figure out that the PDF pinout spec has the backlight + and - reversed. The document is wrong - the bottom of the circuit board labels the + and - and the silkscreen is correct. I've used both the blue backlight and red backlight devices from Sparkfun and the problem with the documentation exists with both.
You should be able to see a very bright light at the right end of the device, underneath and partly extruding from the right under the lens, when it's working. Without that backlight working correctly, the characters are barely discernable and only at certain angles.
In the process of figuring out the polarity issue with the documentation, I had the backlight hooked up backwards - for quite a bit of time while I was trying to find the issue. Once I sorted it out, it fired up fine, so having the polarity reversed didn't seem to cause it problems...it still worked afterwards.
Also, as an FYI, I didn't use 4.2v, I just wired the backlight to 5v. Perhaps that will shorten the life of the display, I don't know, but it works fine and I've run the display for days without any issues.
Anyway, that was my experience with these devices for what it's worth.