Indeed, your question is a very good one because a lot of workers underestimate the danger of ethereal solvents, especially diethyl ether.
Ethereal solvents form peroxide when exposed to air and when concentrated, will leave peroxide residue and explode. Some people may argue that the BHT additives will make the solvent safe but I think this is not true because BHT does not have reducing properties and cannot remove the thus formed peroxide. BHT works by radical scavenger before peroxide is formed.
There are many peroxide test. You can go online and search. One of the ways is to potassium iodide solution combined with starch test to see if there is any elemental iodine formed by oxidation of the iodide by the peroxide.
Take care.