Standard Magento 2.1.2 installation using blank or Luma themes.
Using Safri on a Mac or iPhone clicking the minicart pushes the search box and cart icon over the the left.
The problem seems to be :
<div class="ui-dialog ui-widget ui-widget-content ui-corner-all ui-front mage-dropdown-dialog" tabindex="-1" role="dialog" aria-describedby="ui-id-1" style="display: block;"><div class="block block-minicart empty ui-dialog-content ui-widget-content" data-role="dropdownDialog" id="ui-id-1" style="display: block;">
I don't know where the style="display: block;" is coming from as it is hard coded in the div rather than being in the css. Using the inspector in safari I can change it to style="display: inline-block;" and it works correctly.
Trouble is I can't find where to make the change in the theme files.
Same issue on a clean install of Magento 2.1.3. Safari version 10.0.2. Really weird thing is that if you inspect the element and toggle some style off, it snaps back into place. Wondering if this is some obscure Safari bug.
Was looking at a magento extension demo running Luma and that doesn't suffer the same issue, and I'm trying to see if there is some difference in the CSS. If I figure it out I'll post back here.