A lulav, willow branches, or myrtle branches are only disqualified/pasul if the leaves are so dry that they will crack if you bend them.  Being moldy does not disqualify them.
 

An adult male is wrapped in a talit but one of the tzitziyot is made invalid/pasul.

It is customary to check tefilin twice in each seven year period. Tefilin do not usually require checking, but you should periodically check:

• Tefilin of the type that can become pasul (due to white-washed parchment).
• Tefilin that are moved a lot, such as from place to place where there are large changes in temperature.
• Tefilin in humid climates, such as Florida.

NOTE Ask a sofer for advice about any of these cases.

Torn
In checking tzitzit, determine:

• Are any loops torn?
• Are 8 strings visible on each corner?

If you cannot see 7 strings due to one or more having been torn off, consult a rabbi.

Tangled
There is no problem if tzitzit are tangled. However, to untangle them:

• Is a superior way to fulfill the mitzva, and 
• Allows you to easily check them to see if there are 8 tzitziyot.

Frizzy
If any tzitziyot are so frizzy that the individual tzitziyot cannot be distinguished, they are invalid (pasul).
Note To prevent frizziness during laundering, wrap the tzitziyot tightly in a rubber band before drying them in a dryer, or hang them to dry.
Note

• If the hanging end of a tzitzit string breaks below the lowest knot, the string is kosher.
• If more than one string breaks, or if one string breaks above the lowest knot, consult a rabbi since the tzitzit may not be kosher.