Software is usually verified by some form of hashing scheme like md5, sha-1, or sha-2.
Windows used to run on md5 till it was proven it was horribly broken. A collision could be generated for the typical md5 having two programs have the same md5 disabling the security guarantees it usually provided. Part of stuxnet was believed to be able to overcome the installed package checking mechanisms.
SHA-1 has taken over for verification for a lot of sources including many linux packages. As for it's security it is debatable to a certain extent. There are efforts to port things to sha-2 but it hasn't been officially done yet I think.
Malware persistence is a focus on the malware persisting on the computer or network after infection. It is a very big field considering most organizations use apps from many different software vendors.
When you install an app it can be in source form but it also may contain many different binary(compiled sources). This is problematic. A good example is Hadoop (famous for computing big data problems) contains lots of pre-compiled .jars(java sources compiled).
Static analysis and verification became the go-to standards for a lot of study on verifying binary integrity. But every format and packaged store is different and has different levels of security. There are also more advanced methods or protecting like capabilties(monitoring based on what the apps have access to). A very good minimal for this are some of the libraries released by google including shipshape: https://github.com/google/shipshape
Many companies can no longer get away with just installing a firewall or relying on security products because security is now an "inside problem." Where the software they download from their cloud service(openstack for example) comes from many different vendors. Another example is docker(also many different vendors used to package apps together but provide isolation from the system).
SHA-1 has not been known to be broken, however there are some strange attacks that show that it might be possible it is overcome-able through other means. A prime questionable of how it is overcome example is ssh ebury (http://www.welivesecurity.com/2014/02/21/an-in-depth-analysi... ). SSH ebury seems to be unique in that it during regular execution of the program despite there being no noticeable changes to the user alas from running specific shell commands that are not normally run by regular users it looks not infected/safe.
As for companies installing older versions of software with known remote code execution vulnerabilities or other types of vulnerabilities that are very severe, I do not know of many services or open source software that checks against this! There are however many continuous integration services. Continuous integration services if not done from your company though has problems on verification as well.
A good monitoring practice would be to use homebrew(usually available for most operating systems) to monitor and track what is installed on a regular basis and have some form of whitelist.
Network Traffic analysis for companies is major headache as well. Traffic can be compromised in many different ways. Wikipedia covert channels is a good explanation of some of the complexity involved. There are many tricks for data ex-filtration that make it basically undetectable by normal means (they require some level of active-monitoring). Almost all anti-virus now include network Man-in-the-middle traffic monitoring to do their work.
Anti-virus companies generally have two methods of classifying software as good-ware vs. bad-ware. One is whitelisting and the other is blacklisting. Whitelisting is a selective list of good software. Blacklisting is a selective list of bad-ware. Both methods are generally debatable for which is better. Despite the fact that your anti-virus itself could be compromised usually having an anti-virus provides some level of security.
People despite all this realize that running a company without using pre-made opensource code is rather ridiculous as so much runs on the app stores or third party software sources(outside your company's control).
Security in many cases can be thought of as a castle with multiple walls or layers of defense, but your firewall as being your main wall of defense is a bad decision, because a wall is just what makes your castle stand up to some attacks, it doesn't actively patrol your inner walls for insider threats. Companies need active monitoring systems for access control logs espeically since many common interactions can seem malicious but are just part of people's daily jobs now.
A lot of security is moving to "anomaly detection" where anomalies are jolts of irregularities in the normal business day. Some things that are bad can be parts of normal activity, but done over a longer basis or with extended activity may be hazardous to businesses (a good example is Denial of service attakcs). While anomaly detection is a good trend with smart systems it also suffers from the same "packaging and extending attack surface" like everything else.
This is a short overview of how security works in general, though if you have any questions feel free to ask.