Is it possible to search in the gnome-terminal?

Go to the search menu. Otherwise:

Shift + Ctrl + F

Using grep and its variations

Usually grep is used for plain searching. It would work like this:

make 2&>1 | grep Error

Or if there was a lot of output and you wanted to use a pager:

make 2>&1 | grep Error | less

However, if you want to see all the content, and not just the lines that match your search, you could install the ack-grep package, and then do this:

make 2>&1 | ack-grep --passthru Error 

And if that generates a lot of output and you want to use a pager, you need a bit more syntax to preserve the color:

make 2>&1 | ack-grep --passthru Error --color | less -R

In all the examples I included 2>&1 which merges the STDERR and STDOUT output streams. Otherwise, you would only get STDOUT, which might not include all the errors.

One more variation is just to go straight into a pager and search within that:

make 2>&1 | less

One way to search in less is by typing / to enter a search term. See man less for more searching options.

Using terminal menu

Using the Search menu or a keyboard short-cut Shift+Ctrl+F