J'espère que je vais voir de belles choses.

Rick, it is grammatically wrong. 

However, you may sometimes hear it in informal speech, just as grammatical 'errors' are heard everyday in English !

 "Des" becomes " de/d' " in front of adjectives preceding nouns (French Partitive Articles) 

PS: I just left answering this question to start reading an article in a French newspaper (L'Est Républicain)  - saw this example sentence highlighting what happens with contraction of de and les, as is noted also in the attached lesson - hors de 'les grandes villes' - "hors des grandes villes". Thought it might be interesting and reinforcing ! 

En 2019, 55 % des travailleurs francs-comtois vivent hors des grandes villes. 

PPS: Same 'journal', different article, example of the grammar point questioned initially 

" (ils) .. se sont contentés d'exhiber de larges draps peints des lettres de ... "

It's wrong.

'Des' becomes 'de' before an adjective + noun:

"Des" becomes " de/d' " in front of adjectives preceding nouns (French Partitive Articles)