Blue Flower

If your soap sweats (also known as glycerin dew):

 
Reasons for sweating include:
  • overheating
  • reheating
  • putting in fridge or freezer
  • adding too much additives.
If all else fails, change your base.

 

If your soap is oily or bendy:

you likely added too many additives. Could also be caused by overheating.
If you used too many additives you can remelt with added pure base to dilute.

 

If your soap lost its color, changed color or the colors are blending together:

Liquid dyes will bleed in multicolor soaps. To prevent bleeding, use mica, a colorblock system or colorants like activated charcoal or turmeric.
Turmeric can lose it's color after a while.
Clays can change color in soap.
Any scent oil containing vanilla/vanillin requires the use of either a vanilla stabiliser or a vanilla stable base. Another option is to color your soap brown or black, so if the vanilla turns your soap brown later it won't matter.
Some colorants are not UV proof, so leaving them out into the sun for too long might fade the color.
 

If your layers are breaking up:

Always spray alcohol between layers.
Try scoring the previous layer with a fork before pouring the next layer.
Cut a soap loaf on its side to lessen the pressure on the layers.
 

Small holes on the top or bottom of your soap:

Spray any finely detailed mold with alcohol before pouring, to prevent bubbles.
Spray alcohol immediately after pouring to get rid of any bubbles.
 

Ripples on the surface of your soap:

You moved the molds after pouring, or bumped the table or similar.
You could rub the soap over a wet piece of terry cloth to get rid of the ripples.