DIY EOG (Electrooculography) Circuitry Dangers?
I'd recommend A) use a battery, and B) before you put the electrodes across your eyes, place them someplace with less potential for damage, like your arm.  If it hurts on your arm, don't continue.  

Use disposable pediatric ECG electrodes, if you can get them.

The safest course of action is to isolate the output before hooking it up to an oscilloscope, using something like an Avago HCNR200 (cheap, requires support circuitry) or an isolation amplifier (expensive, but easy), but if it doesn't hurt on your arm, you should be OK.

UPDATE:
Also, don't place the electrodes on somebody w/ implanted electronic devices.  Probably won't do anything, even worst case, but better to avoid the expensive risk of destroying a device.