It's not really a matter of pros and cons. Like a lot of other font packages, mathdesign offers an alternative design for your document. Pros and cons depends on what type of document you want to produce.
With mathdesign fonts, the formulas will be more compact : There is less space around the operators, and the symbols are (most of the time) tinier than in Computer Modern.
But that is not specific to Mathdesign. Most of the recent fonts are in fact tighter than Computer Modern (which is, btw, especially loose).
If you want to use another font than Computer Modern, it is also important to verify that the new font covers all the symbols you need. Mathdesign are quite good at that (all the AMS symbols are present), but other fonts are good too.
If it's important for you to save space, then I suggest you use another font than Computer Modern. Of course, my favorite "other" fonts are Mathdesign, but many of the most recent are very good!
If legibility is you main concern, then CM is a very good choice, since everybody knows it well.
I suggest you look at some comparisons somewhere on the web (for example http://www.tug.dk/FontCatalogue/) and do you own test.
Conclusion: mathdesign's spacing is not bad, it is just tighter than other fonts spacings.