I ran into an issue where the formating conversion from *.Rd -> HTML gets confused in a \tabular environment within the *.Rd when a \code call is used in one (or many) of the elements (cells).
Here is a pseudo-reprex. The back-ticks are converted into \code elements by roxygen2 (\code{b}) and this causes the issue. This should be a 2x2 table, but it results in a 3x2 table. When the \code is removed, everything is fine.
#' Foo
#'
#' A *tabular* test of `pkgdown`.
#'
#' @section: A Table
#' \tabular{lll}{
#' a \tab `b` \cr
#' foo \tab bar \cr
#' }
#' @param x A character string.
#' @export foo
foo <- function(x) print(x)
And the resulting HTML:

The issue might(?) be traced to here:
# correct 2x2 table:
table <- '\\tabular{ll}{a \\tab b \\cr foo \\tab bar}'
pkgdown:::rd2html(table)
# incorrect 3x2 table:
table <- '\\tabular{ll}{a \\tab \\code{b} \\cr foo \\tab bar}'
pkgdown:::rd2html(table)
Note that a new line is generated between "a" and "b" when it shouldn't be.
This might be related to #348 or #630, but I don't think so. Or ... is this intentional and you should not have \code formatting inside elements of tables?
Here's the reprex from above, rendered:
# correct 2x2 table:
table <- '\\tabular{ll}{a \\tab b \\cr foo \\tab bar}'
pkgdown:::rd2html(table)
#> [1] "<table class='table'>" "<tr><td>a</td><td>b</td></tr>"
#> [3] "<tr><td>foo</td><td>bar</td></tr>" "</table>"
# incorrect 3x2 table:
table <- '\\tabular{ll}{a \\tab \\code{b} \\cr foo \\tab bar}'
pkgdown:::rd2html(table)
#> [1] "<table class='table'>"
#> [2] "<tr><td>a</td><td></td></tr>"
#> [3] "<tr><td><code>b</code></td><td></td></tr>"
#> [4] "<tr><td>foo</td><td>bar</td></tr>"
#> [5] "</table>"
Created on 2018-12-05 by the reprex package (v0.2.1)
Just tested it with v1.1.0 and it worked. So if the rest of your pkgdown site setup is back compatible, you can use the old release until the issue is fixed.
(Haven't checked with 1.2.0)
This sounds like a regression, possibly introduced in e1e6e6847e36c83f734baa6ca1627220ba8f9322.
I'm seeing this pop up in my bcbioRNASeq package, but I'm not entirely sure where or how to make a reprex:
Warning in matrix(cell_contents, ncol = length(align), byrow = TRUE) :
data length [15] is not a sub-multiple or multiple of the number of rows [8]
Calls: build_reference ... flatten_para -> <Anonymous> -> .f -> as_html.tag_tabular -> matrix
Seeing the same issue here. I had to downgrade to 1.1, as both 1.2, 1.3, and the development version mangled the tables.
Most helpful comment
Here's the reprex from above, rendered:
Created on 2018-12-05 by the reprex package (v0.2.1)