I am a kindle owner and I face a a lot of issues while converting pdfs that have non-select-able objects to kindle-supported formats via free online software. Is there an application or a website that does this accurately (via OCR, for example)?
PDF is a somewhat problematic format to convert given they way it can be constructed. Given that, I would try using Calibre since it's free. I've used it to manage other eBook formats (of which, there are many it supports). I have not used it to convert from PDF to Mobi. Its list of conversions does list PDF to Mobi, however, there are several warnings about the reliability of the conversion. You can read the limitations on Calibre web site. I would still give it a test.
another free online program to try for converting pdf files to mobi format is this toolkit http://kitpdf.com/ which can provide fast results. More options are also available. Maybe it's a good alternative to Calibre.
I don't know which version of the Kindle you're using.
Willus's k2opt can convert newer pdf formats to Kindle 2 compatible pdf formats, which should also work with newer Kindles. Ghostscript can sometimes do the same, using Compatibility Level 1.4.
If you need to ocr the text, ocrmypdf works for me, using --output-type pdfa-1. I run k2opt first, ocrmypdf second.
If you need to extract text, that's still a bit harder. On the Mac, I've found "PDF to EPUB+" works better than most pdf-to-mobi or pdf-to-epub applications. Then Calibre can convert the Epub to Mobi.