If they directly transfer to your four year college or university, they're not going to care. They'll look at your main diploma/transcript, your GPA, extracurriculars, essays, interviews, etc. If the university you graduated from deem it acceptable to count as credit for your college degree, the grad school will trust their credentialing. I did several accounting classes at a community college my sophomore year of undergrad and i'm not sure my MBA program even looked that closely into my transcripts, and it certainly didn't hurt my ability to get in.
Just like you may have minimum wage, hourly jobs until you get a professional internship, your grad school isn't going to hold it against you on your applications that you didn't always work professional internships. They'll trust that the corporation or organization that hired you for your internship found the other part time work experience relevant enough to transfer into a professional setting.
To Gary's point though, make sure classes directly transfer from the community college so you don't end up having to retake anything and wasting your time and money!