This is a support question, not a bug report.

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some more info:

1. It does NOT happen with the regular upload
2. It does NOT happen if only 1 file was uploaded over Drag&Drop

(server runs on php5.6 with opcache enabled, external memcached instance)

In access log I can see the correct amount of requests when uploading 
multiple attachments. They all send a HTTP 200. URL is:

"POST /services/ajax.php/imp/addAttachment HTTP/1.1" 200 1264

When uploading over the traditional way there is only 1 request for 
all attachments:

"POST 
/services/ajax.php/imp/addAttachment?jsonhtml=1&token=XYZ123XYZ123 
HTTP/1.1" 200 1439

Any ideas what is going wrong?

I've tested it on the demo-horde. There it is not reproducible. I have 
another local installation (same version as the installation with that 
issue) and there is isn't reproducible either.

The version that has this issue uses an external memcached instance. 
Could it be possible that this is a memcached related issue?

I additionally tested with other browsers and can confirm that the 
issue isn't related to browsers (or their version). So it's a backend 
issue.

(German) version of the error message is "Mindestens ein Anhang konnte 
nicht gelöscht werden" if I try to delete the attachment.

Reproducible with:

Version 58.0.3029.110 Built on Ubuntu , running on Ubuntu 17.04 (64-bit)
Version 58.0.3029.110 (64-bit) on Windows 10pro v1607

Cannot reproduce with Chrome 57.

adding multiple attachments via drag & drop is broken with Chrome (Chromium)

Not all files are added although they appear in the attachment list.

You can see that they're not on the server if you try to delete the 
attachment or by sending the email. The sent email does not contain 
the file(s).