How to clean glassware containing pesticide solutions
I like this question because the cleaning of glassware is an often overlooked science in itself. You want to remove "contaminated glassware" as a possible factor in the interpretation of unexpected results in particular. A lot of brain-power and time can be wasted if you cannot assume that all the glassware (and any other surface coming in contact with your reaction) is clean with respect to the compounds of interest, and of any compounds that could interfere with their reaction.

For the given example, since dimetholate is soluble in methanol, methanol would seem to make a good solvent for rinsing the glassware before it dries.  So long as the solute is still dissolved in the solvent, a thorough solvent rinse should be effective with respect to removing dimetholate.  If the solute has dried, even though equilibrium thermodynamics say methanol should re-solublize  anything from the original methanol solution, the kinetics of this can be limiting/prohibitive. If this is the case (i.e. the solution has dried before rinsing), an aqueous detergent scrub followed by a methanol rinse is probably necessary. As water and methanol are miscible, this should not result in any mixed-solvent induced re-precipitation of anything originally present in the methanol-dimetholate solution. 

Keeping to your example, as water an methanol are miscible, even in the case where the solution has not dried you should first rinse with methanol then with DI water. This will ensure any methanol that might precipitate the next standard material will be removed, and any remaining solvent (water in this case) will also not precipitate the water-soluble malathion. 

The process is more complicated when you are using the glassware for a solvent in experiment 1 that is not miscible in experiment 2.  Say you a toluene  solution followed by an aqueous solution. As water and toluene are not miscible, any toluene left over from your toluene rinse would form a 2-phase solution in the aqueous solution.  While you always have the option of thoroughly rinsing then thoroughly drying (with the disadvantage of this discussed above), it is generally more desirable to do the following: thoroughly rinse the first solution in toluene, then rinse that with a solvent that is miscible with both toluene and water, like acetone. After the acetone rinse, then you can rinse the acetone with Di water.  

If you have a reasonably limited number of solvents, it is good to keep a set of glassware dedicated to each solvent matrix. In my experience, the best procedure, and in fact it was part of an SOP for glassware cleaning, was to keep keep the glassware soaking in the solvent for which it will be used, rather than letting it dry.  Obviously this depends on the use case and there are certainly times that it is necessary to thoroughly dry your glassware. But where that is not necessary, to the degree reasonable, I recommend keeping the glassware separated based on what you use it for (i.e. solvent type), and keeping it soaking in that particular solvent.