Sampling too soon after MUX switching channel
It depends on how much capacitance is on the MUX output and how long the ADC needs the value to be stable before beginning the acquisition and conversion. The switching times you see there are not really relevant in most situations. 

If you have a 100n capacitor on the output and the MUX has a worst-case resistance of 270 ohm, then to settle within 1/2 LSB for a 16-bit converter will take around 12 time constants, so about 300usec. If you have a 10K resistor and 100n the time would be about 12ms. 

Your analog anti-aliasing filters should go in front of the multiplexer, of course. 



There is also a small amount of switching noise that will be injected into the output when it switches. Analog switches, especially the ones aimed at precision analog applications, often include a specification for charge injection. The package of charge will be delivered to the output and can cause a relatively large change in output voltage, however it will die off with the same time constant as indicated above. 



This is caused by imbalance in the internal capacitances of the MOSFET switches, coupling a switching transient to the analog switch connections when they are driven on and off.