I'm having similar issues, so I thought I'd add my experience so far.
I get 1 or 2 full charges out of each battery, started with the one that shipped with the Mini. When it happened the first time, I got bounced around quite a bit with Dell support, and eventually received my first replacement battery. Before they would send that out, I was recommended to update the BIOS, so I did to A02.
It didn't solve the issue, so the entire Mini went back to Dell. It returned promptly, with nothing filled out on the "work-performed" sheet of paper. I was told by a tech later that they replaced the motherboard. The Mini came back with BIOS A00, and another new battery, this time of the "KR-" serial number variety, so it was only showing as a 24.4Wh, instead of 32 like the original battery. This battery had the same issue, took a couple of charges, nothing more and the Mini only runs on AC power. I complained about the 24.4Wh battery, had them send yet another battery, and a new AC adapter as well... all with the same result.
The BIOS is up to A03 right now... nothing changed as far as the battery/charging issues.
The Mini is now going back to Dell again... the saga continues.
Items that might be of interest to others:
If the battery has any charge, it shows as Status: Charged (as opposed to Charging). The icon on the taskbar, however, does have the little plug showing, not just the battery.
If the battery has 0% charge, only the battery icon shows.
Design charge: 24.4Wh
I'm tempted to dual-boot with XP to see if XP has the same battery issues, or if it reads the status differently.
Everything so far has been Ubuntu, as it was delivered initially. I did upgrade the repositories to the hardy-netbook-remix sources at one point to see if that made a different also. In the process I think I lost the ability to create a USB rescue media, but I'll cross that bridge when I come to it...