Standalone STM32F030CC minimal configuration
I'm making a PCB with the STM32F030CC microcontroller and have been reading up on the minimal configuration in the datasheet. They don't include a minimal setup diagram [...]


ST typically provide the minimal configuration information in a separate document for each of their MCU families, not in the datasheet. That document usually has "Getting started" as part of the title. For your MCU that document is "AN4325 - Getting started with STM32F030xx and STM32F070xx series hardware development".


  I will be using all 6 UARTs, [...] I will be using the internal oscillator so I won't need any external crystal.


I hope you've considered the HSI (internal oscillator) accuracy limits, temperature drift, and potential need for calibration.


  Do I need to have the ADC filter capacitors as I won't be using the ADC?


I believe you are referring to the capacitors across VDDA and VSSA, and yes, it still makes sense to do that because those pins provide power to other parts of the MCU too (e.g. the "Reset block" and the internal oscillators) not only the ADC.

Unless you are producing something that is extremely cost-sensitive, then you reduce your risk by following the ST guidelines. Note that their reference design (in the document linked above) lists a 1 uF VDDA capacitor in the "mandatory" section. Since the VDDA and VSSA pins are next to each other, it's really easy to added their recommended capacitor there.


  Is there anything essential for it to work that I have missed?


I haven't done a full design review, but one point is that your BOOT0 pin has no pull&#8209;up. So while it is tied to Gnd for booting from the main Flash then fine. However if you ever want BOOT0 to be "high" (e.g. to use the built-in bootloader) then you should not assume a floating BOOT0 pin will be treated as "high".