It might only be a small piece of text, but your career objective is the opener for your CV and the first part of this important document that employers will see. If it has spelling and grammatical errors throughout (particularly if you are applying for a role where you need such skills), it can give employers the sense that the application was rushed, that you don’t have an eye for detail, and that you’re not very thorough, despite claims that you are all those things. Career objectives need to blow employers away from the get-go, not deter them from reading the rest of your CV or application. 

Remember, HOW you write can say just as much about you as WHAT you write.