Unfortunately, the stats provided by the web panel are not likely to be too useful for this purpose, as they just don't provide enough information from your logs.
That said, a particularly high number of requests for your form, or the "mailing" component/function of your CGI script, and the IP's associated with those requests may be indicative of attempted exploits - you just won't be able to tell from the stats if they were successful, or exactly how the exploit was attempted.
For this purpose, looking at your raw log files is a better way to go, as you can see the activity in more detail, such as the timing of IP's visits, the "pattern" in which they surf your pages, and often query strings being passed as part of the request.
If your script is actually being exploited, you will most likely know about it soon enough - the backscatter should start to show up in your inbox and, depending upon how badly the script is compromised, you can expect DH to be shutting down your mail services for potential spamming pending your contacting DH support and taking the steps that are necessary to eliminate the exposure.
The best way to evaluate whether or not a particular script is "exploitable", is a careful inspection of the script by a programmer that understands the security ramifications involved. If you are using a commonly available script, a google search for exploits will often reveal security advisories that are relevant to the script. You could also discuss here the script you are using, and take advantage of the community "brain pool" to help evaluate the security of your script and/or suggest other more secure alternatives if necessary