Is it advisable to emphasize (italicize) good research qualities in a research statement? In a Ph.D. application, a statement of purpose (or more precisely, research statement) is required. I think a candidate should use this statement to showcase his/her good research qualities backed up by the research experience to the admission committee.

In order to make those qualities (i.e., those positive adjectives) stand out, can one emphasize those adjectives by italicizing them?

Specifically, I am referring to qualities such as "independent thinking ability, rigorous"...

In my opinion, the research interests and professors of interest should be highlighted in bold so as to facilitate the faculty reader allocation. This way, highlighting these adjectives also in bold will be pretty messy. So it may be a good idea to highlight the adjectives in another and less catchy form, i.e., the italic form. Am I right?
The preferred details for typesetting your research statement are likely to be highly subjective. Different things are likely to be pleasing, striking, or off-putting, depending on the individual preferences of whoever is reading your application.

I would agree that italics are one of the preferred methods to provide emphasis without being too flashy or distracting. Whether or not that is the appropriate choice for your research statement should probably depend to some extent on the style and content of the rest of your application as well. If you have access to a university writing center, you should try to speak with someone there to decide on the style and arrangement of your application.

To speak to my own experience, I generally will not consider a candidate more capable or skilled in independent thought, rigorous work, or attention to detail, because it is typographically emphasized on their application.