basically you don't like line 426 which says
{\large\color{blockbodyfgcolor}#3}
If it said
{\large\rightskip\z@skip\spaceskip\z@\xspaceskip\z@
\color{blockbodyfgcolor}#3\par}
then you would get justified text (and fix the \par issue of your other question.
It's a bit inconvenient to patch that you could just edit a local, renamed, copy and use that instead, or simpler just put
\rightskip0pt
\spaceskip0pt
\xspaceskip0pt
at the start of your block entry, and
\par
at the end. (The need for \par is a bug in the class file really, so you could report that)
If you do want to patch it, egreg suggests:
\documentclass{tikzposter}
\usepackage{xpatch}
\makeatletter
\xpatchcmd{\block}
{\large\color{blockbodyfgcolor}#3}
{\large\rightskip\z@skip
\spaceskip\z@\xspaceskip\z@
\color{blockbodyfgcolor}#3\par}
{}{}
\makeatother
which would save editing a local copy of the class.
Actually you could just have posted the first two words of the title and not bothered with the example:-)
Bad linespacing in TeX is almost always due to changing the font size but not including the end of paragraph in the same scope, which results in the new size text being set to the original baseline.
In the cited example you need
\block[c]{Columns}{
The page can be divided for some segment of the poster into columns of vertically aligned blocks by using the environment \cmd{ columns}. Within this environment, a column is begun with the command, for instance, \\
\vspace{1em}
\cmd{\bs column\{}0.40\cmd{\}}\\
\vspace{1em}
for a column of blocks center aligned along a vertical line with default width of $40\%$ of the available width.
Following this, additional blocks are created which will be aligned into this column until a new column is called
or the environment is ended. The current column can be used for reference by the variable \cmd{\bs colwidth}.%
\par%<<<<<<<<<<<<<<this par (or a blank line) needed here
}
Probably the definition of \block ought to provide an implicit end of paragraph, but clearly it doesn't so you need to add it explictly.
Best Answer
To change the default vertical spacing between blocks, use the class option
blockverticalspace=<length>. To adjust the position of a single block, you can perhaps setbodyoffsetyandtitleoffsetyin the\blockoptions.