How to search the current word in all opened tabs in Vim?

It's actually the default behaviour although it may be hard to notice: try * then change to another tab and use n ans N in command mode to jump forward and backward between search hits.

This may make more sense if first you turn highlighting on for all hits:

:set hlsearch

 :bufdo vimgrepadd yoursearchterm % | copen

I don't have an exact solution for your problem, hopefully a better answer than mine will come up. But this is how I tackled the problem of finding a word in all buffers.

" enables to search in all open buffers with :Search <pattern>
command! -nargs=1 Search call setqflist([]) | silent bufdo grepadd! <args> %

nnoremap <left>  :cprev<cr>zvzz
nnoremap <right> :cnext<cr>zvzz

The first line creates a command Search with the search pattern as argument, which writes the results in a quickfix list. The two other lines map the (at least for me) useless arrow keys to something useful; they are mapped to jump to the next/previous Search or to the next/previous compile error, etc., they simply step throu the quickfix list. You can use this as follows:

:Search foobar
<right>
<right>
…