No it makes no difference to the meaning, which is the most important thing. I do not care if someone writes 'colour' or 'color', or 'realise' or 'realize'. Like in your question you spelled it 'prioritize', when in the UK we spell it 'prioritise'. It made no difference to my understanding of your question though. However I would say if you are spending time in your work writing professional or formal documents it is probably best to stay consistent in how you spell the words, i.e. pick either the American or British spelling and then stick with it. It would look more professional to be consistent in how you spell things. A problem for example, might be if you spell the same word differently within the same document because you are confused about which one to use. It would be better just to pick one spelling and then stay with it. I'm sure if you look online you will find a list of the differences in spelling, there are not that many. If you really want to improve this aspect I do not think it will be that difficult.

Well, if the question is, "Will we still understand you?", then of course there's no problem. However, if you're wondering whether your writing does sound a bit "off" because of this mixing, then yes we do notice that as well. The important thing here is to pick one style and stick with it. I just did a quick search for style guides (British English) and found this: http://ec.europa.eu/translation/english/guidelines/documents/styleguide_english_dgt_en.pdf I'm pretty sure style guides for US English are as easy to come by. :)

Being American I don't find it annoying at all. I can still make sense of what the word is enough to comprehend the rest of the sentence. It's Okay! :)