Issue 624851  has been merged into this issue.

Re-purposing this to track issues specific to paper-dropdown-menu.

For iron-dropdown issues, see  issue 621731 

Our pattern for paper-dropdown-menu is currently:

  <paper-dropdown-menu>
    <paper-listbox id="permission" class="dropdown-content"
        on-iron-activate="onDropdownMenuIronActivate_">
      <div id="item1" class="dropdown-item" role="option">Item 1</div>
      <div id="item2" class="dropdown-item" role="option">Item 2</div>
    </paper-listbox>
  </paper-dropdown-menu>

According to bicknellr@, WRT behavior near the bottom of the page:

Turns out paper-dropdown-menu passes through a couple properties called `vertical-alignment` and `horizontal-alignment` all the way down to the overlay.

It's still not that awesome, because iron-fit-behavior seems to be set up to *always* align one edge of the given element (the overlay in this case) with the target (the button) but by setting those properties to "auto", it will at least put the dropdown on top if the overlay scrolls and there's more space above than below.

I plan to investigate this further.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/5ee39ec3164fa909ef8209ad33e841cbc632c20d

commit 5ee39ec3164fa909ef8209ad33e841cbc632c20d
Author: stevenjb <stevenjb@chromium.org>
Date: Tue Jul 19 18:43:10 2016

MD Settings: Fix paper/iron dropdown alignment

Default alignment for both paper-dropdown-menu and iron-dropdown
is top/left. The top align behavior is pretty much always undesirable,
especially on laptops with smaller screens.

BUG= 624303 
CQ_INCLUDE_TRYBOTS=master.tryserver.chromium.linux:closure_compilation

Review-Url: https://codereview.chromium.org/2161743002
Cr-Commit-Position: refs/heads/master@{#406332}

[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/bluetooth_page/bluetooth_device_list_item.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/certificate_manager_page/certificate_subentry.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/controls/settings_dropdown_menu.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/device_page/display.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/languages_page/languages_page.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/on_startup_page/startup_url_entry.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/passwords_and_forms_page/address_edit_dialog.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/passwords_and_forms_page/credit_card_edit_dialog.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/search_engines_page/omnibox_extension_entry.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/search_engines_page/search_engine_entry.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/search_page/search_page.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/settings_shared_css.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/site_settings/media_picker.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/site_settings/site_data_details_dialog.html
[modify] https://crrev.com/5ee39ec3164fa909ef8209ad33e841cbc632c20d/chrome/browser/resources/settings/site_settings/site_details_permission.html

@stevenjb: We collided. You closed as fix, and I just linked some other bugs that are directly caused by paper-dropdown-menu issues. Should we re-open until those are fixed in Polymer?

Could you clarify which of the initially described problems still remain? Then go ahead and re-open this.

I don't think that any of the initial issues remain. The title of the bug though is generic and I thought that we can use it to track all outstanding issues related to paper-dropdown-menus.

I'm not a fan of re-purposing bugs. I'll change the title of this one, please file a new issue describing the current symptoms.

Note, there is an issue tracking some of the current dropdown issues:  issue 639718