What are the problems to open a PDF document in Illustrator program?

Illustrator is the best program to edit PDF, it will also save it without increasing massively the file size (unlike photoshop). I personally dont see any issues with opening pdf in illustrator if it is for edit purpose. if it is to view it, use adobe and foxit.

I always use the following script to open multiple pages in illustrator

AI_openMultiPagePDF_CS4_CS5.v1.02.zip

and here is how to install the script into your illustrator program

Installing and Executing Scripts

Hope this will be useful to you to open PDF documents into illustrator.

Thanks

Depends on what software it been created, if it was InDesign, your text will come all broken and not arranged in text boxes. If you dont have the font installed, you will loss all the special characters and the kerning may as well suffer. The transparency effect may come fragmented or blended.  If the file was made from Illustrator, it will come clean as an Illustrator file, unless you have not the fonts. 

There are few problem that i have faced while opening PDF file in illustrator are:

1. Most of the times, the text in PDF covert to graphics and you can't edit it anymore.

2. While opening a PDF file with multiple page in illustrator you can open one page at a time.

3. Sometime the placement of the object and text can shift.