Is there an application that scan the phone or the phone image searching for vulnerability issues?
In the internet there are several tools that make Network scanning, but I found nothing specific for Android.
Any ideas please comment, I'll be very grateful.
Aside from open ports that a network scanner would find, you may also be vulnerable to certain local exploits. The somewhat recently released X-Ray app is designed to check for a number of known vulnerabilities (though it is not capable of fixing them - you'd need an updated version of Android for that).
Almost all of the "one-click root" methods exploit a security hole; it's usually a privilege escalation exploit to get "temp root" as a first step. (From there the scripts will go on to make /system read-write, allow writing to partitions that are normally read-only, etc., in order to keep root access across reboots.)
Obviously, if you can break the security of your phone, someone else can too.
TL;DR: If a root method exists for your phone that does not consist of "unlock the bootloader and flash whatever you want" - you have a security vulnerability.