The minimum legal text size will vary depending on the type of product, where it is going to be sold and the nature of the copy in question. For instance, the Food Industry Regulations in Europe specify that all mandatory legal text (ingredients, allergy warnings, nutritional values, etc) must have a minimum x-height of 1.2mm (unless the pack is very small in which case that drops to 0.9mm). Marketing (or 'romance') copy is not subject to the same rules. In some cases (such as alcohol content) the minimum size is defined by the cap height, but this minimum size also varies from territory to territory. The specific legal minimum for what you are working on should be defined by the technical and/or legal department of the company that you are working for, but a good practice for teeny tiny text is to place a clear, eye-catching note on the artwork (outside the cutter guide) which states the point size, cap height and x-height of the text in question. This makes it easy for approvers to check the artwork and moves the responsibility away from you.
The next question will be whether the small text is actually printable. Again, you should be provided with a print spec from the printers who will produce the labels and this should include minimum printable text size (or two - one for positive text and one for negative, reversed out text) which will probably be expressed in points. HOWEVER, take that with a grain of salt because the print spec will also include a minimum printable line weight (two again - pos and neg) so if your text is so small that the lines making it up fall below the minimum line weight then you will have to thicken it up a bit, probably by adding a very fine stroke if a suitable heavier weight is not available or appropriate. This is particularly import with reversed or white out text which can 'fill in' when printed.
Finally, there are the aesthetics and readability. Unfortunately, these always tend to suffer when we are required to put a gallon into a pint pot - which is all too often the case with text on packaging. The best you can do is usually to use a condensed version of the type face and squeeze up the leading (I usually stop just before the ascenders and descenders start to crash into each other). This allows the actually point size to be as big as possible.
As one of the other questions says, you have to learn not to let the ugly appearance upset you to much. This is a common situation in packaging and product labelling and is only likely to get worse as packaging gets smaller (for good environmental reasons) and the amount of legally required copy gets bigger (for good consumer protection reasons).