When someone uses Speak with Dead on a corpse, the spell says that you can ask the corpse up to five questions. Asking implies that the corpse can hear you.

What I want to know is whether or not the corpse's other senses are intact?

1. Could I show the corpse a picture and ask them to describe it?




2. Could I put a flower to a corpses nose and ask them to tell me what
   they smell?




3. Could I write down the five questions and get the corpse to read
   them?

The reason I am asking is because, during a session I was DMing, I ruled that the corpse could not read the scroll that the party was showing them. But after the session, the ruling I made felt unfinished. I need to make sure I took everything into account and didn't flub the ruling.

The rules don't specify operating senses

This is a decent case for relying on "spells do what they say they do" and keeping the interaction simple. Here is what the spell will do.

You grant the semblance of life and Intelligence to a corpse of your
choice within range, allowing it to answer the questions you pose. The
corpse must still have a mouth and can’t be Undead. The spell fails if
the corpse was the target of this spell within the last 10 days. (Basic Rules, p. 105)

The corpse is not alive, it has "the semblance of life" and Intelligence. Intelligence is described as being the key attribute for memory.

The corpse knows only what it knew in life, including the languages
it knew.

Memory being required to recall what it knew in life fits Intelligence being magically activated.

Intelligence Measures: Mental acuity, information recall, analytical
skill (Basic Rules, p. 10)

Intelligence, measuring reasoning and memory(Basic Rules, p. 60)

bolding mine

The magic allows the otherwise dead corpse to answer your questions. Beyond that, the spell description doesn't activate, nor reanimate, anything else.

Your ruling was correct

You are the DM (per your comment). You ruled that the corpse could not read the scroll; your ruling captured the spell's powers correctly. If you want go beyond that at your table, it's your call.
Rules as Fun...

None

The corpse has no access to senses, including hearing. The caster magically has interactive access to its memories, but it has no access to its environment at all.

Speak with dead magically asks the questions of the corpse. It makes it seem alive again, but it says this is only a cosmetic seeming, not real (“the semblance of life and intelligence”). It doesn’t grant implied hearing—if it granted hearing it would say so explicitly, with something like, “restores hearing to the corpse for the duration”.

The spell lets the caster ask questions and get answers that the corpse knew in life. They can’t add anything to its knowledge and then ask it questions about what was(n’t) just added: it can’t be taught new things.

It is explicitly unaware of what’s happening during the spell:

the corpse can't learn new information, doesn't comprehend anything that has happened since it died

… including during the spell.

Only the magic of the spell allows the questions—only the questions—to penetrate. The spell basically magically extracts existing information from the corpse using an intuitive voice-activated interface, not actually allows the caster to deal with a thinking creature.

So:

1. The caster can ask it to describe a picture it knew in life. They can’t show it something it hasn’t seen before and ask questions about it.




2. The caster can ask what it remembers roses smell like. They can’t place a new flower under its dead nose and ask it questions about the new flower.




3. The caster can ask it what was written on a paper it knew in life. They can’t show it a new paper and ask questions about the new thing.

Ask the DM

The spell description indicates that the corpse can speak. All other details are up to the DM. The fact that you can ask the corpse questions arguably implies that the corpse can hear (or that the spell allows you to transmit questions to it in some other way), but even this is up to interpretation.

It can if it can see and knows the language

If the corpse still has it's eyes it should be able to see as the spell gives it a semblance of life and intelligence. If the scroll is written in a language that the creature knew in life it will be able to read it since that is knowledge it had in life.

The corpse not being able to learn won't prevent it from being able to read the contents of a scroll. It just won't be able to learn from the information in the scroll. For example if the scroll contains the BBEG's plans to retreat to their hidden base, you can't ask the corpse to guess where the base might be given the contents of the scroll. It can only tell you what it actually knew in life.