How to better indent multiline strings with many string formatting args?
How about this?

def log_exception(self, exc_info):

    msg = ''

    msg += 'Time:                 %s\n' % datetime.now()
    msg += 'Path:                 %s\n' % request.path
    msg += 'HTTP Method:          %s\n' % request.method
    msg += 'POST_ARGS:            %s\n' % request.form
    msg += 'GET_ARGS:             %s\n' % request.args
    msg += 'Client IP Address:    %s\n' % request.remote_addr
    msg += 'User Agent:           %s\n' % request.user_agent.string
    msg += 'User Platform:        %s\n' % request.user_agent.platform
    msg += 'User Browser:         %s\n' % request.user_agent.browser
    msg += 'User Browser Version: %s\n' % request.user_agent.version
    msg += 'Username:             %s\n' % current_user
    msg += 'Email:                %s\n' % getattr(current_user, 'email', 'no email')

    self.logger.error(msg, exc_info=exc_info)


I guess, logging an exception doesn't happen every often, so efficiency shouldn't be a concern.

Alternatively, you can emulate variable interpolation and avoid formatting altogether:

now = datetime.now()    
email = getattr(current_user, 'email', 'no email')

msg = _('''\
    Time:                 {now}
    Path:                 {request.path}
    HTTP Method:          {request.method}
    POST_ARGS:            {request.form}
    GET_ARGS:             {request.args}
    Client IP Address:    {request.remote_addr}
    User Agent:           {request.user_agent.string}
    User Platform:        {request.user_agent.platform}
    User Browser:         {request.user_agent.browser}
    User Browser Version: {request.user_agent.version}
    Username:             {current_user}
    Email:                {email}
''')

self.logger.error(dedent(msg), exc_info=exc_info)