I am building a simple power source OR-ing circuit using two Schottky diodes like the one below. Source 1 is a 3.7V lithium-ion battery and Source 2 is a 6V 1W solar cell. I can see that the two diodes make it such that the load is provided current from only one source at any time (ideally) and that current is prevented from flowing back into the inactive source. But say, one of the diodes is omitted. What are the consequences of current backflow?
The consequences of reverse current flow depend on the power source - some can handle more current (and voltage) than others.
Your 6V panel probably consists of 12 cells in series (equivalent to 12 forward-biased silicon diodes) so it will draw excessive current when the voltage exceeds 7.2V. However a 3.7V Lithium-ion battery is only 4.2V when fully charged, so you could safely eliminate the diode in series with the solar panel.
Your Lithium-ion battery may be able to take all the current that the panel can produce, but it must be not be charged above 4.2V (or it will explode!). The panel can put out up to 7.2V, so you need a diode in series with the battery to prevent it from being overcharged.
Another reason for using diodes is if one or both of the power sources is connected externally, and you want to prevent damage due to a short circuit at the socket or source connected with reverse polarity.