This is why lab exercises are important. I remember first building some actual TTL circuits on bread board, I learned very quickly that this whole digital stuff is a lot uglier and messier than on paper or in the simulator.
With sharp rise times, synced up to a common clock, even after soldering in a whole bunch of capacitors, you can still stick a probe pretty much anywhere and see switching spikes all over the place, from power rails to completely unrelated signals that are supposed to be stable. Using actual TTL, there was another funny lesson what this weird "fanout" value in the datasheet meant.
A similar lesson I learned that way (and a very memorable one :-)) was about flyback diodes.
Ah, but that may well be because of your scope probe's leads! The sharper the edge the more likely that will happen. That's what those shitty little springs are for that come with your scope probe: you disconnect the ground wire and put that spring on the naked scope probe pin around the ground collar. Then where you want to measure you use the pin to go to the signal and the little spring to reach the nearest ground. Presto: clean signal (or at least, much cleaner). Also, make sure to tune your probe (that's what the little plastic screwdriver with metal tip is for, there is a small trimmer in the probe you can reach through a hole and that is critical at high frequencies) and avoid probes with switchable 1/10 like the plague, over time the switches go lame and then you'll be tracking all kinds of weird gremlins.
This is just reminding me of the time I played with an oscilloscope, touched the probe against my finger and found my body was antenna picking up mains frequency.