The Raspberry Pi will show (on the HDMI output) a small rainbow square in the upper right corner, when an under voltage is detected (check Power FAQ).
The first revisions of the Raspberry Pi have polyfuses (F1+F2) on the USB-A ports which limit the current. In later revisions these fuses were replaced by 0 ohm jumpers. However there is still a polyfuse (F1) on the bottom side under the micro USB power port. When powering the board via this port and a high current is drawn then the voltage drop through the fuse can get to high and problems can occur. See also the Troubleshooting Guide.
Depending on the system USB+LAN can be deactivated/activated with the following commands:
$ echo 0 > /sys/devices/platform/bcm2708_usb/buspower $ echo 1 > /sys/devices/platform/bcm2708_usb/buspower
$ echo 0 > /sys/devices/platform/soc/3f980000.usb/buspower $ echo 1 > /sys/devices/platform/soc/3f980000.usb/buspower
If you do not have the permission, then run it with sudo, e.g.
$ sudo bash -c 'echo 0 > /sys/devices/platform/bcm2708_usb/buspower'