Thank you for the quick response!

I downloaded and installed the DotNetNuke 5 version, but the problem is still there.

Uploads result in an error popup with a message "http error1 :0:"

Chrome Developer tools shows an error message: 

POST http://domain/Default.aspx?tabid=543&ctl=Edit&mid=1740&UseUploadModule=Dynamic&_Namespace=RTE&_UploadID=dnn_ctr1740_EditHTML_txtContent_txtContent_UploaderImage_1366785551054_1&_UploadControlID=dnn$ctr1740$EditHTML$txtContent$txtContent$Uploader&ContextValue=!3wEWAQUQQzpcV2luZG93c1xURU1QXBWsFrpTgeHRxvNRBJAWnkWLLa!3A&_MaxSizeKB=1024&_VFN=testtemplate.html&_Addon=verify&_AddonGuid=49236F06-03F1-B00C-5B30-35245893135C
Ox562
Ox55e
Oxb3
Ox55d
Ox53c
Ox53a
(anonymous function)
Ox5b2