Moss: Moss has a winter active cycle and reaches its peak growth in February and March. It normally turns brown and goes dormant in summer. It is most common in thin lawns, which may be the result of excessive shade, prolonged summer drought stress, and/or lack of adequate fertilizer nitrogen to maintain dense turf. Just maintaining dense turf year around will dramatically reduce the moss population in most lawns.

 The most popular treatment for moss control in lawns is Moss Out (ferric sulfate). The liquid formulation is most effective in my experience. Moss Out is a contact killer that turns moss almost black overnight. It also turns the grass dark green for a short time so an application can be very dramatic. Unfortunately, Moss Out rarely kills the moss completely and it comes back again next winter. Also the metallic odor can be objectionable for several days after application. It is not clear if the iron sulfate is toxic to birds.

 A more environmentally friendly approach involves renting a dethatching machine and using it to physically remove the moss by going over the lawn several times at different angles. After raking off the debris, follow with a nitrogen fertilizer application to stimulate the grass to grow back and thicken the lawn. Ammonium sulfate at 5 lbs of product per 1000 sq ft will work well. It is a soluble salt so watering it in after application will dissolve it and wash it into the soil where birds will not come in contact with it. Mid-April is a good time to use this procedure.

 Dandelions and clover: Most broadleaf herbicides for selective control of weeds in lawns are mixtures of 2,4-D, Mecoprop, and Dicamba. One example available at Home Depot is Spectracide Lawn Weed Stop. This mixture will control dandelions of all types and is fairly effective in controlling clover when used properly. The attached information sheets point out that these herbicides are relatively non-toxic to birds when used as directed.

Strategically, I suggest you start weed control in the fall around early to mid-September. This way you avoid the spring period when birds are nesting and most active on the lawn. If you use a ready to use formulation of this product you can spot spray individual plants of dandelions and reduce the amount of herbicide birds might come in contact with.

There are several different clovers that may infest lawns. At this time of the year the only actively growing clover is a winter annual clover (Strawberry clover). It germinates in fall and grows vigorously through winter before flowering in late spring and dying. It is also best controlled with fall sprays on the young seedling plants.

If you have a serious weed population in your lawn it may take a couple of years of repeated treatments to reduce the population below your threshold level. Once you have controlled most of the dandelions it is fairly easy to keep them under control by maintaining dense turf year around (by applying fertilizer 2 - 4 times per year, depending on your lawn) and using wood chisel or other weeding tool to hand dig the dandelions that remain. The goal is to remove as much of the tap root as possible when you dig them out and to be consistent in your efforts.

You may even want to plant white clover (Trifolium repens) in your lawn to reduce the need for nitrogen fertilizers and to increase summer drought tolerance. You can find lawn adapted white mini and micro clovers by searching on line. 

Good luck.