Usually the headline of the goals exactly shows what our sims should do. The text below often causes confusion, but includes hints, if a goal is not completed as expected. If the game is played with another language, the translation may also cause confusion. (It might help to change the language within the game for a moment.) For some goals the times aren't mentioned correct.
For the German version there is an article at Akshaya's inofficial Sims FreePlay guide -Translating mistakes, Stumbling Blocks and complicated goals.
Für die deutsche Spielversion gibt es einen Artikel in Akshayas inoffiziellem Sims FreiSpiel Guide:
Schwierige Aufgaben in der wöchentlichen Quest
Here are some goals, which I found complicated.
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Make Tai Chi at park Go to the park, tap your sim and choose Tai Chi
Reach Nirwana Go to the park, tap your sim and choose Reach Nirvana
Make Tai Chi at park at 7.00 (p.m.)
You can either start at 7.01 p.m., according to my experience the goal completes immediately,
or follow Palmjill's experience:
Or try both, and see which way works for youPalmjill wrote:You need to finish the goal at 7 pm ie. start at 6 pm. You get an hours' leeway so start anytime between 6 and 7. Remember you have to see your sim complete the action at the right time too.

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Watch a movie at midnight
This goal will be completed at midnight (between 12.01 am and 12.59 am)
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Edit according to Perturbee's post below:
(Face-)slap a sim: works only with nemesis status
Fake handshake a sim: works only with enemy status
Make a fake handslap with another sim. (Sorry, I don't know whether the wording is correct)
I found this action by random for a Game Center goal, which asked for an enemy.
It can be done between two sims, who don't like each other and we have to be rude, if we want to see this (un)social action.
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Have a toddler in a kiddie pool. There are two goals, one asks for the kiddie pool at the swimming center, the other for the kiddie pool at home.
In case you don't have a toddler: Both can be completed with a preteen.
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Relax in a poolchair. First I've sent my sim in an inflatable chair in the pool, but
this goal is finished with a pool recliner.
There is another goal, which asks for the inflatable chair, but it's mentioned clear
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Have 6 sims a nap. Hint in text: „Time for siesta“
This works from 12.01 pm until (I'm not sure about 3.00 pm, I haven't been patient enough to wait^^)
Edit Oct. 19th 2017: This task may complete at any time now.
Plant Garlic between 8pm and 6am (Edit dec. 17)
Completes at the beginning, if you start at 6.01pm (6.38 also works)
It also completes at the end, if you visit your sim when he's done with planting between the mentioned times.
More infos for this goal are on page 5 of this thread, posts from Palmjill, calleighwolfe and me, dec. 6 until dec. 17.
Edit 26 March 2014:
Changes at social goals with "Life dreams" update.
Become Nemesis
Date a sim
If you send a sim, who has the required relationship either at a neighbor's town or in your own town, these goals should complete instantly.
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May/June 2015
New with the Dream Homes update
Make a sim hibernate In my game this did not complete with a baby nor with a toddler.
The sim had to be at least a preteen.
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April 2016
Seriously Swing
Open the textbox and read the hint. In my game this task has to be done at the mall.
Submit a creation to the Firemonkeys There is no need to actually do that! The task completes as soon as you tap the real estate sign. After that you'll get a second pop up for the terms of service. If you don't want to submit your creation you can tap "no".
If you miss the sign, send a sim to work at the Real Estate Agency; the sign will then show up next to the postbox.
Max out needs, inspire a sim. Note: Whatever you do to complete this task, it may not work if you try it with a sim that is inspired by Rainbow Cake slices.
Apparently this goal doesn't work if we just inspire any sim. At least one need has to be really down. The easiest way is to drop down the hygiene until the sim has the ugly green cloud arround. So, have a sim kick a trash can and pick up the dirt or send him into a dirty pool until he's "stinky". Then max out all the needs until he's pretty sparkling.
Oct. 2017
Take single photo at the mall
Choose „Use photo booth“