"I suspect our staff is mixing lubricants before they are even used. Is there a simple way to determine this?"
Unfortunately, there is not an easy way to tell if lubricants have been mixed unless they have vastly different viscosities, such as ISO 32 and ISO 680. You then most likely would see a thickening or thinning of the lubricant. Also, if a red automatic transmission fluid (ATF) was mixed with an engine oil, there might be some type of color change.
However, there is one way to find out if the lubricant's viscosity has been affected without having to employ a laboratory. It involves a viscometer or a Visgage, which is a viscosity comparator that uses the falling ball viscosity measurement concept. Its principle of operation is based on comparing the viscosity of the test fluid with a reference fluid of known viscosity. The Visgage is also a good tool to have on hand for checking whether new oils coming into your facility are what you ordered.
Other than using this method, you will need to find a reputable lab to establish a baseline for the lubricants and then have the suspect lubricant tested. Once this has been completed, you can compare the results and make a definitive conclusion. Depending on the quantity of lubricant involved, this type of testing may be cost-prohibitive or just not make good sense. It might be more efficient to simply dispose of the lubricant and start again.
The best solution would be to avoid this problem in the first place by having trained staff members and well-labeled/color-coded equipment. Using a different sealable and reusable container for each lubricant can help to prevent cross-contamination.
Keep in mind that mixing oils can have far-reaching effects. For instance, even if two gear oils are the same viscosity and have similar additive packages, one may have sulfur-phosphorus extreme-pressure (EP) additives. These can be detrimental to a worm gearbox with brass gears, as the sulfur-phosphorus EP additives are too aggressive on softer yellow metals due to the length of contact between the teeth of the bull and worm gears.
In some cases, this may not be a major problem, especially if the lubricants are the same type and have the same base oil and additive package but are just different brands. Nevertheless, for peace of mind, when in doubt, change it out.