Sounds like there must be some other anion in your water that really likes the metals.  Probably phosphate or sulfate?  Did you check the conductivity of your water?  Should be 18 Mohm.  

If you can't figure it out easily, it's always an option to leave the metals separate, and add them to 1x concentration into the culture medium as needed.  This greatly reduced concentration should eliminate precipitation.

Also, and this depends on what you're doing, these metals are not necessarily needed for many E. coli applications.   You'll basically need them only if you work under strictly chemically defined conditions, and/or if your protein has a known requirement for one of the metals, e.g. in the active site (in that case, just use the one metal that you know you need!).  

Studier for example went all OCD in his papers, trying to forumlate a medium that would work for every special case of metal-dependent recombinant proteins that you could possibly want.  But if you have a normal (metal-independent) protein, and you're using a complex matrix like yeast extract or tryptone in your medium, these will have all the trace metals your E. coli needs.  

Using tap water instead of distilled water is a good trick to include trace elements too. 

Conductivity on the MilliQ water reads 18.2 Mohm. But one of the individual metal bottles might be contaminated with extra anions.  My supervisor has decided (to my relief) we will just use normal LB media and IPTG induction for now, and I'll try making autoinduction media again at a later date. Thanks.

I absolutely agree with John, I get the feeling that preparing the entire 1000X trace metals mix is not needed in most situations. In my own work I've just used FeCl3 and CaCl2 and have never had a problem. The ZY will provide most of the trace metals you need.

I think that the source of the white precipitate could be the formation of CaSO4 (kps~10-4). My suggestion is to add the Ca2+ salts separately and keep the pH for the other solutions (these that contain the rest of the metals) around 5,

Studier himself wrote that even for the defined media usually you can use just 100 uM FeCl3 to have the same high density (apparently, the traces of metals in the reagents are sufficient for E. coli unless you overexpress some protein with a specific metal dependence):

"The highest iron concentration tested, 500 μM, showed no evidence of toxicity. In a defined medium containing 100 μM FeCl3, omission of the metal mix only slightly diminished the maximum density and the level of target protein produced by auto-induction, so 100 μM FeCl3 may suffice for many purposes if a suitable metal mix is not available.

In contrast to the results summarized in Table 5, manganese or cobalt, alone or in combination, did not compensate for a deficiency in iron in subsequent experiments. A difference was that the media used in the tests reported in Table 5 contained seven different vitamins but subsequent experiments contained no added vitamins. Whether the presence of vitamins could account for the difference has not been tested."