I'm writing the final piece of an adventure right now. In it, the party will be co-opted into a wizard's experiment. The wizard knows that beholders spawn and create new beholders by dreaming of themselves or a rival. The wizard believes that, by entering the "dream plane", it should be possible to interfere with the dream and disrupt the spawning process.

My question is: any ideas for random effects which might affect the party on the "dream plane"? E.g. hallucinations, strange bodily transformations etc?

To put this into context, my basic plan for this part of the adventure is:

- Wizard creates portal into "dream plane" - during the ritual party must fight of demonic incursions from other planes, randomly determined

- Party enters "dream plane" whilst wizard holds portal open. They are subject to all sorts of random effects. There is no sense of direction and they must navigate by sounds

- Party finds beholder guarding its "mind palace", i.e. a manifestation of its subconscious mind

- Party must defeat beholder, gain entry to the mind palace and solve a puzzle to disrupt the spawning process. They may also find a crystal representing the beholder's soul, which they can destroy. Doing so creates a storm in the dream plane which they must escape.

If you have read The Wheel of Time series by Robert Jordan I would recommend you take inspiration from that.  Telaranhoid   (sp?) as he calls the dream world has its own properties, visitors there can do the things they normally would be able to do in the waking world but the real power there comes in the ability to manipulate the dream world itself, something dreamers and some natural denizens are able to do to some extent depending on how familiar with it they are, able to do things with a thought that otherwise would be impossible.  One thing in particular involves entering someone else's dream, you can get trapped there until the host allows you to leave, to the point of no longer being aware that you're dreamwalking at all, essentially slipping into a dreamlike state.  Other things involve nightmares that spin out of control and travel the dream world as essentially a torrent of chaos. You could assume the beholder is a gifted dreamer able to reshape the dream into pretty much anything imaginable.  Maybe you could apply psonics  to the dream world if you're not using it anywhere else in your campaign.  I'm thinking  of the old 2nd edition psionic dueling rules, don't recall them specifically but I remember if you weren't a psionicist  you were SOL  in a duel.  Of course there's always the mundane shifting environment which happens in all dreams, or the falling dream, stuff like that.

I always seem to have dreams I can fly, or I see through other peoples eyes. It might be fun if in the dream world the players switch bodies, they are seeing the experience through one of the other party members (dreamers) eyes. Given that nightmares are manifestations of our own insecurities, maybe this would be a good time to play on the characters flaws. The Beholder in his dream world thinks up scenarios that test the characters on a personal level. (ex. I have a character that loves his spirits too much, the beholder maybe creates an illusion that he falls into a giant wine cask, and he literally could drink himself to death unless the group can figure out how to  help him escape own vice). 

People often fear deformity, dismemberment, or defiling of body parts. So having folks hands or arms elongate or fall off, noses slip from faces, eyeballs dangle from socket, etc could all be very terrifying. Things like getting old and decrepit would be easy enough to incorporate, so maybe the characters pass through an area where they seem to age at a rapid pace, their stats take a temporary hit as their minds and bones become old and brittle. Make them fight something at their level that would normally be a pushover but they realize in their weakened state that these monsters might be too much for them now. If the journey to the palace is long enough and they have to rest along the journey, have them find the "residence" of a fellow dreamer, go all Hotel California on them :)

I love dream sequences, the twisted imagery, the probing at the very soul of the character. It's awesome.

It's a dream.  Realism is even more optional than usual.  Have you ever read The Hitchhiker's Guide to the Galaxy by Douglas Adams? 

This is a really awesome idea. The first place I'd think to pull inspiration from is American McGee's Alice.

Thanks all, some good suggestions! I will draw on these to create a random effects table. This part of the adventure comes right at the end, so by then I should hopefully know enough about the characters to create some "personalised" dream elements/nightmares for them... mwahaaha

I know this isn't the exact advice you were looking for, but be sure to keep in mind how Beholders are born.  If you haven't read through that portion of Volo's, effectively if a beholder dreams of another beholder, it could bring one into existence.  So just in case that comes up, or in case your beholder is also having some some sort of dream beyond what is going on in the dream world they've entered.  It could be interesting.  Also, for more inspiration on that, take a look here.

Sounds like your looking for some lair effects. 

Reverse Gravity, launch the party up into the air for a round. Take falling damage at start of next round.

Vertigo. Beholder rotates floors to walls. Disadvantage for any action as the Beholder rotates the reality, maybe a Dex save to avoid.

Mirage. Use Silent Image or Phantasmal Force against the party. Make a copy of the Beholder, a minion, or something psychedelic or twisted a beholder would think of