I'm running Boinc 7.2.42, the latest version for Linux. The GPU was working, but I updated the CUDA & Nvidia packages with apt-get, restarted, now BOINC fails to recognise the GPU, citing error code 65280.

The GPUs work. CUDA-Z sees my GTX 690. The driver module is loaded:
$ ls /dev/nv*
/dev/nvidia0 /dev/nvidia1 /dev/nvidiactl /dev/nvidia-uvm

So why does BOINC's GPU support suck?

BOINC event log:
Mon 22 Dec 2014 10:51:25 AM EST | | Starting BOINC client version 7.2.42 for x86_64-pc-linux-gnu
Mon 22 Dec 2014 10:51:25 AM EST | | log flags: file_xfer, sched_ops, task
Mon 22 Dec 2014 10:51:25 AM EST | | Libraries: libcurl/7.35.0 OpenSSL/1.0.1f zlib/1.2.8 libidn/1.28 librtmp/2.3
Mon 22 Dec 2014 10:51:25 AM EST | | Data directory: /var/lib/boinc-client
Mon 22 Dec 2014 10:51:25 AM EST | | GPU detection failed. error code 65280
Mon 22 Dec 2014 10:51:25 AM EST | | No usable GPUs found

The GPU was working, but I updated the CUDA & Nvidia packages with apt-get, restarted, now BOINC fails to recognise the GPU, citing error code 65280.

The error code is not a BOINC error code, even though it is BOINC that shows it. GPU detection failed. error code xxxxx is the code thrown by the drivers, all BOINC does is relay that to you. Error code 65280 looks to me that there was no OpenCL detected.

I just wonder, if your GPU was working, why did you feel the need to update your drivers?
When stating that you updated the drivers with apt-get, it would be nice if you said what steps you followed, and on what distro this is, so others can check if the package even contains the necessary CUDA and OpenCL components. Lack those and BOINC won't detect the GPU.

So why does BOINC's GPU support suck?

BOINC has splendid GPU support as long as it can detect the drivers OK. It works on all the platforms and it used to work on your system prior to you updating the drivers, so why blame BOINC? Why not blame it on the drivers? Can't you have forgotten something, like adding the user to the video group?

I'd say read through http://docs.nvidia.com/cuda/cuda-getting-started-guide-for-linux/#axzz3MfPjhau0 which details how one can install CUDA drivers correctly for the various distros.

If you want help, honey gathers more bees than throwing mud does.
Start again, explain what you did, which steps you followed, did you e.g. uninstall the previous package or did you just install the new one over this one? Did you install an SDK?

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That's odd, since I did install the Nvidia OpenCL packages. Also, the project that uses the GPU uses CUDA, and is able to find the shared libraries:
einsteinbinary_BRP4G_1.39_x86_64-pc-linux-gnu__BRP4G-cuda32-nv270:
linux-vdso.so.1 => (0x00007fff44ef0000)
libcufft.so.3 => /usr/lib/x86_64-linux-gnu/libcufft.so.3 (0x00007f1cd76e2000)
libcudart.so.3 => /usr/lib/x86_64-linux-gnu/libcudart.so.3 (0x00007f1cd7495000)
libcuda.so.1 => /usr/lib/x86_64-linux-gnu/libcuda.so.1 (0x00007f1cd6532000)
libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007f1cd6314000)
libm.so.6 => /lib/x86_64-linux-gnu/libm.so.6 (0x00007f1cd600e000)
libstdc++.so.6 => /usr/lib/x86_64-linux-gnu/libstdc++.so.6 (0x00007f1cd5d09000)
libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007f1cd5943000)
/lib64/ld-linux-x86-64.so.2 (0x00007f1cdc25e000)
libdl.so.2 => /lib/x86_64-linux-gnu/libdl.so.2 (0x00007f1cd573f000)
librt.so.1 => /lib/x86_64-linux-gnu/librt.so.1 (0x00007f1cd5536000)
libgcc_s.so.1 => /lib/x86_64-linux-gnu/libgcc_s.so.1 (0x00007f1cd5320000)
libz.so.1 => /lib/x86_64-linux-gnu/libz.so.1 (0x00007f1cd5107000)

I didn't think updating the packages would break anything. And they were kernel updates, not nvidia package updates. I am able to see that the card is present, drivers are loaded properly, and I can run CUDA applications.