Whether to use mulch or compost on flower beds is a question of what you want to accomplish and how quickly.  Technically, mulch is anything you put down on the soil to prevent weeds and loss of moisture from occurring and to improve the looks of the area.  So compost applied to the surface of a garden bed is mulch, the same as wood chips or shredded leaves or small stones or other such items.  

The results of what you add as mulch are different, depending on the material used.  Shredded wood chips or bark will help prevent weeds and retain moisture in the beds.  They break down slowly, eventually becoming a single-source compost.  This will slowly add organic matter to the soil and supply a minor amount of nutrients.  They also last longer than compost due to the larger size particles.  Typical compost (either homemade or commercial) has already been broken down by microbes and the nutrient content, although minor, is more quickly available to the plants.  It does a poor job of weed suppression but helps retain moisture.

The best of both worlds would be a layer of compost covered by a more decorative layer of shredded bark or wood chips.  A total of three inches is enough to prevent most weeds and to help retain moisture during our typical summer dry season.  Be aware that homemade compost often has weed seeds in it that may germinate whereas commercial compost has usually been heated enough to kill any seeds.

The mushrooms growing in the mulched areas are the fruiting parts of fungi that are decomposing the wood chips.  They are not harmful but can be removed if they are unsightly.  They will eventually decay and go back into the soil food web if left alone. 

This publication gives a lot of good information on compost in the home garden and this publication details kinds and uses of mulch materials. If you have additional questions on this subject, please use the reply feature within this email or call the Chesterfield Extension office at<personal data hidden>.  Thanks for using Ask an Expert!