As an avid toki pona user, I've often contrasted it with NSM and noticed things that are really tough to express in toki pona (very likely intentionally).

One thing is that toki pona has no built-in comparatives at all. A usual thing is to say something like

mi sona e ijo mute ala. jan pi pali sama li sona e ijo mute.

'I know not many things. My colleague knows many things.'

ona li suli taso mi suli mute.

'She is big, but I am very big.'

jan ni li jo e mani mute. taso jan ante li jo e mani mute mute.

'This person has a lot of money. But the other person has lots and lots of money.'

Another thing is that there's no built-in way to make a relative clause at all.

mi sona e toki. mama meli mi li sona e toki sama.

'I know a language. My mother knows the same language.' (As opposed to 'My mother knows a/the language that I know'!)

mi sona e toki. mama meli mi li sona ala e toki ni.

'I know a language. My mother does not know this language.' (As opposed to 'I know a language that my mother doesn't (know)'!)

ona li pali e ijo. mi sona e jan ante. jan ni li pali kin e ijo ni.

'She does something. I know another person. This person also does this thing.' (As opposed to 'I know another person who does what she does'.)

moku mute li kama tan soweli. mi moku ala e moku ni.

'Many foods come from animals. I don't eat these foods.' (As opposed to 'I don't eat foods that come from animals'.)

It's also extremely tricky to construct specific tenses and specific logical conditions. The particle "la" can mean "when", "because", "also", or "if", and is only supposed to be used once per sentence. This is especially challenging when trying to contrast things that have happened with hypothetical conditions. For example

jan olin ona mije li moli la mi mute li pilin ike.

I intend this to mean 'we feel bad because his romantic partner died' but we can't really disambiguate, for example, 'we will feel bad when his romantic partner dies' or 'if his romantic partner dies, we will feel bad'.

You can qualify things with "tenpo pini/ni/kama la" ('in past/this/future time'), but you're not supposed to use more than one "la" in the same sentence, so it's discouraged to write things like

?tenpo pini la mi moku e ni la insa mi li pilin ike.

'Because, in the past, I ate this, my belly feels bad.'

You can try to break these up into multiple sentences.

tenpo pini la mi moku e moku jaki. mi pali e ni la mi kama pilin ike.

'In the past, I ate gross food. Since I did this, I started feeling bad.'

This gets really challenging if you have to refer to several different things of the same sort, which perhaps have conditional relations to one another that apply at different times or in different circumstances. For example, if you wanted to say "when my mother arrived, the plane that she was on was very warm because it had a broken air conditioning unit which the crew didn't know how to fix", you might end up making a long series of sentences that tell a story.

tenpo pini la mama mi li kama kepeken ilo tawa kon.
ona li kama la kon lon ilo li seli mute.
ni li kama tan ni: ilo lete li pakala. jan pali li sona ala pona e ilo lete.

In the past, my mother came using an air travel tool.
When she/it arrived, the air in the tool was very hot.
This happened because of this: the cooling tool broke. Workers did not know how to improve the cooling tool.

But some kinds of conditions don't necessarily lend themselves well to this form, like if I wanted to say "if she had known that this would happen, she wouldn't have taken this airplane", or quantifiers like "every Singaporean who goes to school in Singapore learns English and whatever the government defines as his or her family's language" or "everyone who was inside the building when the earthquake happened got injured by some object"...

I don't feel confident about my ability to describe the truth conditions of the latter two examples in toki pona in a way that's faithful to the English original.

It's also unclear to what extent we're allowed to stack "e ni:" and "tan ni:" in order to embed indirect discourse and chained reasons.

?ona li pilin pona tan ni: toki pona li pona tawa ona tan ni: ona li toki lili li jo ala e nimi mute.

'She was happy because of this: she liked toki pona because of this: it's a small language and doesn't have many words.'

Edit: also, NSM explications assume that you're deliberately defining new vocabulary in order to expand your language, which isn't really customary in toki pona. Even if we figure out how to express a concept or situation in toki pona, we don't then acquire a single word that we can use for that concept or situation in the future.