No parseInt is not causing a problem here.
Here's a fiddle to demonstrate that the code works: http://jsfiddle.net/sZXJ8/
HTML:
<div class="next" id="next1"></div>
JS:
var id_next = 1;
$('.next').attr('id','next'+parseInt(Number(id_next)-1), 10); // Always include a radix when using parseInt
alert($('#next0').length);
Your problem is elsewhere.