How would one go about identifying unknown cell cycle checkpoint proteins (i.e., cyclins)?
I've actually been involved in a hunt for checkpoint proteins in diatoms (a type of eukaryotic algae), the cyclin family has been greatly expanded in these organisms and we were trying to figure what these extra cyclins were sensing/signalling[1]. 

In a nutshell, the first author looked at different conditions which were likely to affect cyclin expression. Most of these conditions prevented cell division (e.g. lack of nutrients, G2/M chemical inhibitors or light) and samples were taken before and after the blocking conditions were removed. Afterwards mRNA's were quantified of suspected cell cycle genes. As the checkpoint genes' mRNA and protein cycles extremely transiently this took some doing. Cyclins that reacted to the conditions were characterised using complementation assays and other techniques.

Afterwards yeast two hybrid assays were used to identify interacting proteins to build up the network[2]. In general, these experiments were not that straightforward and messing with essential genes causes a lot of trouble but it still nothing compared to the original yeast cyclin work where they were slogging through mountains of temperature sensitive mutants defective in their cell cycle (see the work of Lee Hartwell and Paul Nurse who got the Nobel prize for this in 2001 with Tim Hunt).