hook_menu_alter per node type

We can't see your complete code, but you need to make sure the hook_menu_alter is calling another function to get the $node, rather than loading the node in the hook, where it will only be done when the menu is rebuilt.

For example, here I'm changing the title of the "View" tab when the node type is "vehicle".

<?php

function custom_menu_alter(&$items) {
  $items['node/%node/view']['title'] = custom_node_view_tab();
  $items['node/%node']['title'] = custom_node_view_tab();
}

function custom_node_view_tab() {
  $node = menu_get_object();
  if ($node->type == 'vehicle') {
    return 'Stats';
  }
  return 'View';
}
?>

this solution won't work, in fact it doesn't change anything if you use another function or set the menu items in the hook. if you think about it this makes sense, because if the hook is cached, it won't be called again, therefore your extra function won't get called too. i've tried the following to verify it (it tries to disable a menu item of the bbb module only if the node type is "classroom"):

function foo_menu_alter(&$items)
{
    $items['node/%node/meeting/attend'] = foo_meeting_attend_button();
}
function foo_meeting_attend_button()
{
  $node = menu_get_object();
  if ($node->type == 'classroom') {
  	return false;
  }
  return array
  (
    'title' => 'Attend Meeting',
    'page callback' => 'bbb_join',
    'page arguments' => array(1, 3),
    'access callback' => 'bbb_access_attendee',
    'access arguments' => array(1),
    'type' => MENU_LOCAL_TASK,
  );
}

after clearing all caches, everything works as expected and the menu item is disabled if i go to a classroom node page. now theres two ways to check if its really dynamic or if it is coming from cache. first, just access another page with these menu items with a different node type, or change the node type "classroom" to something else in the code. now, without clearing the cache, access the page, and you will see, that the data comes from cache. so even the node type is not classroom, the menu item is disabled, or if you change the node type name to something else, and refresh the classroom node page, it stays disabled.

i am still looking for a solution for this, if someone has any idea, it will be greatly appreciated.

Yes, of course it doesn't work! I didn't test it thoroughly. Thanks for the catch. I'll reply again when I have a soution.

Yeah actually you have to access the title callback property, not the title. Then you can do something like this:

function somemodule_menu_alter(&$items) {     
$items['node/%node/edit']['title callback'] = 'override_edit_title';
$items['node/%node/edit']['title arguments'] = array(1);
}

//Change "Edit" tabname to "Modify" for pages of your_content_type
function override_edit_title($node) {
  if ($node->type == 'your_content_type') {
    return t('Modify');
  }
//else return the default name
  else {
    return t('Edit');
  }
}