It's important to ensure that your water is fit for purpose and, if in a regulatory environment, production and testing of the water should match the specification. Millipore has plenty of free advice on their website, and offer a diverse range of Milli-Q systems for labs.
Generally, for chromatography, the specifications are fairly simple, eg Milli-Q, tested to ACS/ASTM, EP, USP etc. The issue of trace contaminants really depends on what the water is being used for. The limits are different if you are performing Ion Chromatography, trace inorganics, trace organics, etc.
TOC is increasingly being specified for pharmaceutical HPLC applications, however, as Krickos noted, some systems can take a lot of flushing/recirculation to reduce the value, and if you are performing some analyses, eg halogenated pesticides, TOC may not be appropriate. If you examine the specification for bottled pure water, you will often find they offer different Ultrapure grades for different applications.
For chromatography they may perform UV gradient testing, UV spectrum, fluorescence, residue, and bug count/specific conductance at time of bottling.
UV gradient testing using a known good solvent ( I prefer acetonitrile - the method is usually listed in the monograph ) is a simple technique that can provide baseline data to help identify the origin of peaks and high background in the future.
Lab units, such as Milli-Q configured for chromatography, are maintained and serviced according the the supplier, and the product water tested according tro the regulator. The qualify of the feed water into the unit is one of the main determinants of final water quality.
I assume your laboratory water supply has been "fit for purpose" until now, so applying expensive control criteria and buying new purification systems may not be justified, but it's certainly worth raising with your management, and performing a risk assessment, even if no change is planned.
For problem solving, it's convenient to have two sources of pure laboratory water to help exclude water issues.
It's also really important to ensure that the containers the water is being dispensed into are also of suitable quality and cleanliness. Pure water is a universal aggressive solvent - ask any corrosion engineer.