Did members of the Africa Corps commit any notable war crimes during the course of the North Africa campaign? What about the Allies?

While I can't comment on the Allies, the Afrika Korps did commit war crimes. I have written about Rommel before here and adapted from that:

Research on Libya remains immensely difficult. Before the civil war, it was virtually impossible to access the German files in Libya, especially those of the consulate, that could give much needed information. Post civil war, it remains unclear if the files even still exist. Furthermore, Africa has still received little attention from researchers, especially Anglo researchers except on Rommel himself who is one of the most misrepresented figures in history.

Anyways, in November 1942 when the Germans took over Libya, there was a pogrom in Beghazi in which members of the Afrika Korps participated and that left 67 people dead. Similarly, members of the German Afrika Korps advised the Italian administration on setting up a concentration camp system where the 3.500 Jews of Libya were interred and at least 600 died due to poor living conditions.

In Tunesia, a similar situation presented itself, where German soldiers were involved in plundering several Ghettos in the country as well as in setting a Jewish council and blackmailing the Jewish community for 90 million Francs for the German war effort. They also again assisted in setting up concentration camps together with the Italian administration. The German Afrika Korps also assisted in organizing deportations of Jews from Tunis, mostly of British citizenship, who were forcibly removed from their home first to Italy and then finally to the Innsbruck Reichenau camp. There, they were imprisoned and forced to do labor.

Furthermore, they also worked closely with the Einsatzgruppe Afrika, lead by Walter Rauff, inventor of the gas van. While planning the Holocaust in Palestine, they mostly used Jews for forced labor in Tunisia to build up fortifications against the British. There is also the case of the Afriak Korps murdering Jewish POWs who had served with the Jewish Brigade of the British Army. 500 POWs, most of German or Austrian origin, were executed by members of the Afrika Korps.

So, generally, against the myth that the Afrika Korps were somehow clean, they did committ numerous war crimes and atrocities and were closely involved in the Holocaust by organizing deportations and ghettoization as well as internment in Italian run camps.

Sources:

Wolfgang Proske: „Ich bin nicht beteiligt am Attentat“: Erwin Rommel, in: Proske. (ed.): Täter Helfer Trittbrettfahrer. NS-Belastete von der Ostalb, Münster/Ulm 2010.
Maurice M. Roumani,: The Jews of Libya. Coexistence, Persecution, Resettlement. Brighton/Portland (UK) 2009.
Klaus-Michael Mallmann and Martin Cüppers: "Beseitigung der jüdisch-nationalen Heimstätte in Palästina." Das Einsatzkommando bei der Panzerarmee Afrika 1942. In: Jürgen Matthäus und Klaus-Michael Mallmann (ed.): Deutsche, Juden, Völkermord. Der Holocaust als Geschichte und Gegenwart, Darmstadt 2006, p. 153–176.
Klaus-Michael Mallmann and Martin Cüppers: Halbmond und Hakenkreuz. Das Dritte Reich, die Araber und Palästina, Darmstadt 2007; published in English as "Nazi Palestine: The Plans for the Extermination of the Jews of Palestine", New York 2009.