There are a few redstone glitches. They can be tricky to avoid, but advanced redstone engineers often use them in their advantage.
Visual wire glitchEdit
One of the most common glitches; the wire looks like it goes straight into the block, but it doesn't power it. This oddity is often abused in compact redstone circuits.
N/S repeater quirkEdit
When this repeater is built facing north/south, it will only have 1 tick delay. This is caused by the way redstone updates are calculated. Before repeaters were added, this was mainly used to open double doors in 1 tick.
Repeater block update issueEdit
This same issue is the case for note blocks. Note blocks won't sound when the repeater turns on, unless there is a wire next to the note block. If the repeater is powered by a wire or a torch, the note block will sound at the same time as the wire or torch update, before the repeater updates. If, on the other hand, the repeater if powered by any other input source, the note block will never make any sound.
Dispenser update glitchEdit
When a dispenser is powered by redstone, any other redstone related block update will cause the dispenser to activate, meaning either to tick or spit out an item. This can be used to detect redstone block placement around the dispenser, hidden from view. A rapid pulsar will cause 2 updates per pulse, both when turning on and turning off.
Repeater connection failureEdit
A repeater won't connect with a redstone wire. This causes some problems with single piece wires not powering a block properly. This has been fixed in 1.7.
Visual glass glitchEdit
When glass is used to block off 2 redstone wires. Visually the wires will be broken apart, though they will still transfer power though the glass block.