The L1/L2 issue:

Using two receivers on different frequencies delivers greater accuracy. Without getting into one of my long technical pieces, what EdB said above about radio waves when penetrating the ionosphere is absolutely true - all the time. The sunspot issue simply makes the changes in the ionosphere more pronounced and violent (leading sometimes to such high levels of low-level ionization that lower-frequency transmissions, eg, below 1GHz, are impossible).

You can get some idea of what the ionospheric "weather" is doing by going to this website

http://www.swpc.noaa.gov/ 

In Ye Olde Days, we'd listen to WWV, the NIST standard time/frequency station. WWV also broadcasts GPS system outages, down to the individual satellite level. In between these solar/GPS/sunspot status reports, you can listen to time go by, one second at a time.

The problem these propagation issues impart to GPS is a variable "propagation delay" from when the signal is transmitted by the GPS bird to when it is received at your receiver. GPS is critically dependent upon knowing this time delay; that's why GPS clocks are so accurate and have such a high resolution.

You can achieve a higher resolution idea of what the true prop delay is by using what is called a "diversity receiver" - there are three types of diversity: spatial, frequency and time. Your L1/L2 receivers are using frequency diversity. This reduces the "jitter" in propagation delay because the ionosphere doesn't effect both frequencies equally at the exact same time. By reducing the net "jitter" in the prop delay by use of diversity reception, you achieve a higher level of accuracy.