For scale-ups, it's essential to become a learning organization, putting its learnings into practice. So, improving your processes becomes a job in itself.
There are many well-know tools to organize this, like the PDCA cycle, all the way up to Agile, Lean and TQM systems. This blog has a nice little overview of those.
However, for a relatively small organization, it's usually better to keep it really simple and just make one person responsible for overseeing a particular practical improvement. Set them a deadline and monitor if and how the desired improvement is happening. It shouldn't have to take more than a couple of weeks at the most.
In many organizations big and small, professionals well kow that some things are not going as they should, but too often no-one does anything about it – or is aware that they can do something about it. Systems tweaks are easy enough, but changes in behavior may be a little harder to address.
By turning improvements into individual tasks, appointing one ‘owner’ and using deadlines, you will prevent much of inaction. You don’t want to run the risk of past mistakes slowly creeping into the DNA of your company.