The annoying broadleaf weed is Common Mallow. Get ground damp and pull.
http://www.colostate.edu/Depts/CoopExt/4DMG/Weed/mallow.htm
Pointy leaves, purple flowers and dense seed puffs is Canadian Thistle. Paint leaves with herbicide.
http://www.colostate.edu/Depts/CoopExt/4DMG/Weed/canad1.htm
The succulent in the cracks and edge of the grass is Purslane. Easily pulled when young.
http://www.colostate.edu/Depts/CoopExt/4DMG/Weed/pursl1.htm
The quick growing vine that climbs fences and plants id Bindweed. Paint with herbicide.
http://www.colostate.edu/Depts/CoopExt/4DMG/Weed/bindw1.htm
It looks like the clover looking weed with dark leaves too is Black Medic. Easily pulled from damp lawns.
http://www.colostate.edu/Depts/CoopExt/4DMG/Weed/black.htm
Lawn care fact sheet.
http://www.ext.colostate.edu/pubs/garden/07202.html
The “paint leaves” is where you want to keep the underlying or surrounding vegetation. For gravel or fence, just spray. The blue Bayer stuff works well.