to get your drop box folders to show up in your gallery you have to go to settings>accounts>dropbox and click "sync now" to sync drop box to your phone. this is different than just going to your apps and clicking on the drop box icon. your phone and drop box account are LINKED because basically they are both logged in to your online dropbrox ACCOUNT. but when you actually SYNC your phone to drop box you can see whats going on in each account in real time, see changes in real time etc. so if you take a picture while synced, it will appear of course in your normal gallery folder and then as soon as its uploaded to drop box you will see it in the dropbox sync folder too. the drop box sync folder in your gallery will have the drop box logo in the lower left corner. the pay off comes when you have things in your drop box that have been added from locations other than your phone. if you have a pic or video on your Pc or laptop AND have the drop box app on your pc or lap top, you can drag/drop or copy paste into the PC/laptop dropbox folder and then access it from your gallery in your phone. or you could be at a friends house and log onto your online dropbox and upload pics over the internet, the content will show in your gallery on mobile :O) so with sync you get that immediate access thru other programs or apps instead of having to go to the dropbox mobile app each time.
i found this out because i had some thumbnails and icons in my drop box gallery sync folder from hell that just WOULD NOT GO AWAY. when i cleared out my dropbox on my pc, it also cleared out my online storage (which is what i wanted because i ran out of space online, i just use drop box as insurance because i hate losing photos and videos. i always save my stuff on MY HARDWARE.). so once i had my drop box emptied, the sync folder should have been emptied too but it wasnt. i went into my android file browser and deleted the thumbnails etc but the emptied photos were STILL in the sync folder. i checked my mobile app, i logged in online, and i checked my desktop app and all 3 clearly said i had no photos in any of them. i could not find out where these thumbnails were coming from.
i literally had to go to settings> application manager in my SG4 and clear the data and cache from the drop box mobile app AND uninstall the mobile app from my phone and start over after restarting the entire phone SMH. when i did this, i had to restore all my settings. so i literally had to "turn on uploads", "turn on upload over wifi and mobile data", set up passcode and the whole 9, i literally started from scratch. when i thought i was done, i noticed the drop box folder wasnt in my SG4 gallery anymore. i was about to get mad at drop box because i shouldnt have had to do any of that anyway. i went to "settings>what to display" in my SG4 gallery and the drop box checkbox was greyed out as not being an option. the drop box app didnt have a setting for displaying a folder on mobile at all, so by chance i went to "settings>accounts" and then clicked on drop box. it had an option to "sync now" so i clicked it and my drop box folder was back in my gallery and up to date. for now, all 4 links (mobile, sync, online, and PC) have the exact same contents.
looking in hind sight, i may have been able to just toggle the "sync now" button in "settings>accounts>dropbox" . but i just wanted to post this because im sure someone else will find this info helpful. and if the quick way doesnt work, you still have the long way that worked for me.