There are many in the livestock industry that claim that dung analysis is the most accurate method to determine animal mineral deficiencies. It is certainly more immediate compared to hair analysis which typically records the mineral status of an animal from a few months previous. Blood analysis can be helpful, but tends to be difficult and costly to obtain. It is also important to remember that blood only transports minerals, so does not necessarily reflect the actual tissue mineral status - ie the working end of the animal (N.B. hair is a form of body tissue). 

Soil analyses are probably the least reliable option as minerals that appear to be present in soil are often 'locked-up' and not available to plants. For example you may have plenty of magnesium showing up in a soil test, but little in the plant, and therefore very little in the animal. Leaf tests may give bit more of a reliable clue (though are often limited to testing only a single plant species at a time), but there is nothing like getting it from the so-called 'horses mouth' - the animal itself. The following instructions for dung analysis for cattle have been extracted from the Queensland's DPI&F website: