The causes of chatter that you are experiencing have been nicely dealt
with by others.
The problem of separation of parts of the tissue.:
You did not,  believe mention the tissues that you were sectioning on
the cryostat.
Separation can occur between the support medium such as OCT. If you look
at the block carefully you can often see fine hairline cracks. This can
be overcome to a limited extent by soaking in OCT for a few minutes
before freezing. Freezing itself can also cause cracking, especially if
the tissue is large.
Sometimes cracks occur without any rational explanation, I believe that
there is a parallel universe with an anti-histologist bent on causing us
such problems.
The composition of the tissue can result in separation of parts of the
tissue from each other. Tissues with interfaces such as skin can
separate at the junctions between the tissues (skin at the
epidermal/dermal junction)  because of the differences in composition
and hardness of the two tissues.
Tissues such as spleen have little, apart from the capsule, to keep them
together, as spleen is essentially a bag of cells with a fragile
internal support system. It is common therefore to get such tissue
showing cracks across the cells. In fact with tissue containing numerous
"free cells" it is not uncommon to see such cells displaced from their
original location and ending up on parts of the slide in which there is
no section. This can occur even after paraffin processing. Tissues
containing a mixture of fibers and cells often do not show such
artifacts because the tissue is more cohesive.
Barry