No it's usually that some questions in some courses are made by people who are really only very proficient in one of the languages and not so much in the other. Apparently they don't have contributors proficient in each language looking out for this because it's pretty common in Duolingo.
Generally I don't type the proper accents either as I am too lazy and normally it is okay.
The problem here of course is that 'muncă' is 'work' and 'munca' is 'the work', so it becomes a grammar error, not just a spelling error.
If you are on the website then the accented vowels and consonants should appear on the screen near the typing field for easy access. If you are using the app on a phone/tablet you can very quickly install a Romanian keyboard which gives you access to these letters at the touch of button.
I do not know if you have it available already, but I had to copy the internet adress of the Duolingo on Chrome... you go to the settings, select the option to send the Duolingo's main page to the main screen on the phone, and you will be have a Duolingo's icon on your screen... that's the way I practice romanian in beta... because with that option, you use de desktop version, but, going directly to the Duolingo's webpage (it's like if you use your mobile app).
If you use the Android app, using a keyboard like SwiftKey will let you use multiple languages on one keyboard. For example, I have Danish, English, Romanian and German on Danish QWERTY but with all four languages supported and auto-detected for autocorrect.
On PC I also have Danish keyboard layout, but I took a sheet of envelope stickers and wrote the Romanian letters with diacritics as well as the most common symbols and stuck them on the corresponding keys after consulting with an image of Romanian keyboard layout. The letters and symbols I have are:
ă î ș ț â / ? ( ) - =
Those get 99% of tasks done for me, whatever I need to do in Romanian practice.