Posters are not made to last. They tend to be printed on low quality paper with little thought that someone may one day cherish them and wish to preserve them.
TEARS
Tears occur due to the low structural integrity of paper in combination with frequent, heavy handling. You can read an in depth discussion on how to handle posters to avoid tears, creases and crush marks, here.
But if it's a done deal and your poster has been torn, remedial action can be taken to repair the damage by applying a local tear repair or by lining the poster (or both). Etc. etc.
It is imperative that tear repairs are never, under any circumstances, undertaken using pressure sensitive (self-adhesive) tape. Speaking of which...
TAPE
For the most part, posters aren't considered to be fine art right out of the box, and usually don't get their own specialised conservation framing straight away. Instead, they tend to be first be displayed in other ways using blu tack, tape, pins and other m. By the time a poster is considered valuable, tape may have damaged or stained the paper/media.
There are a number of methods that we use to remove tape and any associated discolouration: blah blah
CREASES AND FOLDS
Many poster collectors have a love/hate relationship with folds in their posters. On the one hand, the folds can be evidence of authenticity. For example, many movie posters were folded in specific ways at the time of manufacture and the absence of this distinctive fold pattern may be useful in identifying forgeries. On the other hand, folds are often deep and sometimes run through important aspects of the image or text, detracting from the aesthetic value of the poster. Additionally, many folds occur after the time of manufacture and are simply unwanted reminders of a history of rough handling.
Lining is good. Humidification and pressing is good.
WATER DAMAGE
Mould, stains, blah blah.