Running Android apps@PC
There are other aspects as well - many Android applications are designed in the smartphone form factor in mind. While many work quite OK on tablets, stretching this to a desktop (1024x768 -> 1920x1080) might be a bit too much. Basically, you would get either really big icons (if they were specified as % of screen height/width) or really small ones (if their size was hardcoded in pixel). Also any non-vector graphics that gets resized would look like crap - either blurred or blocky, depending on the scaling algorithm.
There can be also issues with text input - but as some Android devices have a hardware keyboard, it might be not that hard to connect the normal input methods to the Android environment. Not sure about more advanced issues though (runtime layout switching, unicode handling etc.).
Regarding touch input - unless your monitor is a touchscreen (or maybe you have multitouch touchpad) you can't use any multitouch gestures, which some applications might be dependent on. But as there are also single-touch Android devices on the market, this might not be that much of a problem as the mainstream developers probably provide fall-backs for them.
And the other way around - forget about using middle/right click & the scroll wheel. No Android applications have any notions of it. Also no on-hover help bubbles due to how touch input works. Some of it would be probably possible to fake back in (simulating up/down swipe on list widgets, long press on right click, etc.) but it would be far from consistent.
Also, your PC mostly doesn't have all the sensors (accelerometer, magnetometer, gyroscope, light sensor, GPS, IRDA, NFC, camera) that actually make many applications useful.
While I'm not saying it is completely pointless to do so (why not do it if it's possible ), I think the general usability of the Android applications running on PC might not be that high.
Things might change if the developers took PCs in accounts as their targets or if more standard desktop Linux libraries and toolkits can be used for writing Android applications (the Necessitas project is already working on this, it is also possible to use Python to write Android GUI applications Its just still a little unpolished though. )