The e-mail field full of warning signs shown in your screen shot is not normal behavior. Contact form 7 uses Javascript for email validation. Your screen shot indicates that you have a series of Javascript errors occuring at this point.
This is most likely due to a Javascript conflict with either your current WordPress theme or one of the other plugins you are using – see Contact Form 7 Email Issues – there is a link there that covers Javascript Conflicts.
Use Firebug or Chrome Dev Tools to examine Javascript conflicts in detail.
Remember that a problem in one script can cause issues in another.
For example, some jQuery errors can stop jQuery processing any more script, which can make the culprit hard to find. A jQuery error in one of your plugins or your themes javascript files can stop jQuery processing before it gets to the CF7 script.
I am having the same problem. I have several fields that are required. I have an error box popup over the top of that field if it has been left blank or not valid. Version 3.5.4 worked great. I installed v3.6 as i was waiting for the recaptcha fix and now a user must refresh the whole page to enter the missing or invalid fields instead of just having the error box disappear when the mouse hovers over. I am not seeing any JS errors. I am using WP 3.6
Had no clue what script could interfere with the form. Tried everything. So had to install another plugin. I’m waiting for a new release to try again with CF7.
RE: now a user must refresh the whole page to enter the missing or invalid fields instead of just having the error box
@darwood – Floating validation tip has been removed for accessibility improvement. See the chengelog of v3.6.
See also http://wordpress.org/support/topic/validation-errors-dont-disappear-when-trying-to-correct-form-field
@88001002261 – New releases of CF7 are unlikely to change your situation. Any issue you have is almost certainly due to something on your local WP install.
There are so many poorly written themes and plugins that cause Javascript conflicts with popular well written plugins like CF7.
See http://wiki.simple-press.com/installation/troubleshooting/plugin-conflicts/ for general guidance.