I have a 555 setup in monostable mode.
I probed the output (pin 3) and the capacitor (pins 6 &7) to channels 1 and 2 respectively. The waveform looks like the one in the datasheet except I get some noise after the capacitor is charged up. I've attached the scope output image. (Attachment Link)
My values for R1 and C1 are 1M and .1uF.
Is this a concerning result and if so, what should I change to fix the issue?
It is not unusual to get a bit of "overshoot" or "undershoot" with fairly sharp transitions in "real life".
If you reduce the time/div & just look at the transitions, you will probably find they are sinusoidal.
Because you are using a fairly long time/div setting, the 'scope makes a sort of "best guess"of the waveshape, hence the "squarish" look .
On reflection, they are also low amplitude, so accurate representation of them will also be limited by the resolution of your ADC, so you will probably need to reduce the volts/div control as well.