Can too many components on one outlet affect the sound of an amp?

You can break it down to the basics.  Current & voltage coming from any outlet will contain some form of noise, some more than others due to what is plugged into that same line circuit.  What and the only thing that could affect the sound quality from audio equipment is AC noise introduced on the line.  The rest is a current supply issue.  Eliminate the AC noise component and you have clean audio.  Most all floor / wall outlets are 20 amp circuits. Lighting is 15 amp circuit which it should be.  But I have seen where lighting circuits are tied into the wall outlets which is a big NO-NO.  Power conditioners/isolators like Monster Power etc. are a very good idea.  And a dedicated 20 AMP circuit as mention in another post for your power amplifier is also a very good idea.  Ground loops are death to audio systems, and are sometimes difficult to track down.  I have seen special duplexes for audio equipment sold for 500.00 plus.  What a joke!  save your money, a beefy 20 AMP duplex for 1.15 will convey the current and voltage to your piece of gear just as well as the touted special outlet, for ungodly amounts of money.  One other thing all homes have 14-2 gage wire for lighting circuits and 12-2 gage wire for all outlet circuits.  Or they better be to be in compliance with local code.

cleeds
"do you mean the safety ground------"
The ground is lifted only for the outlets in the audio, not from the main circuit board. You are absolutely right that it does not meet the code, when I sell the house, it will be set right. Therefore, I recommended caution. not for every one. It did make a significant difference though in sound. 

Try running your amp direct in the wall. Run your source gear and pre amp off the conditioner. Next separate digital from analog gear if possible.

To begin...an outlet is an outlet.  All are required to be 15 amp rated and all they do is pass power.  You can't hear any difference from one brand of outlet to another. Just make sure the integrity of the outlet is good and not old and fatigued.
Is it better to have multiple outlets on different circuits than just one?  Really depends on how many amps your main power amp will draw during critical demands or sustained demands.  If you are not listening at ridiculous spl's with inefficient speakers then I doubt that this is making any significant difference.  
One thing to keep in mind is the psychoacoustic difference between listening to music with a video source engaged and without.  Music is always more involving without any video content or visual distraction.
The power consumption of your other sources (video) will be negligible.
Other considerations are the quality of your AC coming into your home.  Power demands go up during evening hours.  Secondly, you can check your main service panel for power issues by using a multimeter.  Check both sides of your panel...they should be within 1-2 Volts of each other.  If not you could have an issue with your neutral wire or something else.

A dedicated circuit with sufficient amps to provide at least 10% greater current than you think you need is one of a number of beneficial power upgrades you can make. Plugging a properly sized and actually capable power conditioner into that circuit will not only protect your gear from noise, spikes and transients but it will provide a buffer of power in the transformer/caps to feed the gear when it plays prolonged loud or very dynamic passages. If you are over-subscribing the number of devices plugged into one power conditioner, it is time to get a second one and split the difference... but beware of ground problems if your components are no longer on the same ground.

I absolutely swear by my various generations of PS Audio Powerplants and DIY audiophile-recipe power cables. All my systems now have a completely black background with zero zero zero noise. I monitor the power consumption of representative music and listening levels and you can see and hear the difference that an oversized power conditioner can make.