Wanting to try clipless, I purchased some used mountain bike shoes and was given a used pair of pedals just to see if I would like them or not without spending too much $$$. Anyway, I did okay on my first day but have a few questions:

1) there seems to be some play when clipped in and can wiggle my foot a bit before it pops out. This play seems rather excessive and was wondering if my foot should be more secure? Do pedals and/or cleats wear out and would getting new cleats fix things?

2) I have the Shimano type of pedals and was wondering if the egg beater type would have a bigger "sweet spot" when trying to clip in? Right now in order to chip in I have to be at the "exact" location before my shoe can lock in. It would be nice to just be in the "general vicinity" before getting locked in. Or is this normal and I would just have to get used to it?

3) do the egg beater pedals have a tension adjustment on them? Being a newbie, I think I would like them to be a little loose in the beginning.

TIA..

The first generation clip-less did not allow for side-to-side foot movement which usually led to knee pain. The play you discuss may be to your advantage.

I had Eggbeaters pedals a few years back and if I remember correctly they have ~20 degrees of float so your foot will move all around.
If you want two sided pedals with less float then try Speedplay Zero. But they only work with road shoes.

As far as side-to-side play, called "float".

According to the notes I've read, the standard SH-51 cleats have about 4 degrees of float, and the SF-56 Multirelease cleats have zero (or minimal) float. I haven't tried them as I pull up at times, and need to be well locked in.

As churnman mentioned, a little float is more forgiving on the pedal setup, and may be good for the knees.

It just takes time to learn the sweet spot to clip in. Most SPD pedals are double sided, but a few are single sided and require flipping & clipping.

Yes, a little free play can be a good thing.
If there is too much, it may be that the cleats are worn, or the pedal retention mechanism needs to be adjusted a bit tighter.

Don't worry about being able to clip in and out quickly and easily, it will come with practice. I have used any number of clipless pedal systems, and no matter how they are designed, it takes time before you learn how to get in and out quickly.

If you are using Shimano SPD cleats which are silver colored, there is supposed to be some play in them. Some rotational play is normal, if your shoes are locked to the pedals, then everything is fine. If you don't like the play, you can switch to the black colored cleats, which are designed not to move around. But when you use these type of cleats, you really need to know how to properly set them up to avoid discomfort and possible knee pain.

Egg beaters don't have tension adjustment. But I've never missed it.
I run EB on all my bikes, but if I were to start over, I'd go with Time pedals instead. EBs are great at mud/snow clearing but needs a surprising amount of upkeep for being pedals. Not that its either difficult, expensive or hideously time consuming. But it is one more chore that needs to be done regularly.
If I didn't encounter mud or snow I'd probably stay with Shimano instead.

I'm one of the few riders who wants zero float. On my Look pedals, this is accomplished by using black cleats, rather than red cleats.

In addition to the "float" issue, note that most pedals including most Shimano mtn bike "spd" pedals allow you to adjust how much tension is on the release. People new to pedals may want to back off the tension (normall a very, very small allen wrench is used near a spring on the pedal) so you can pop out with very little effort. If you ride aggressively, standing, sprinting and such that may not be a good idea as you don't want to come out of the pedals unexpectedly but it's something to be aware of and understand if your pedals do indeed allow that adjustment.

I prefer the Crank Brothers Candy pedals over the egg beaters just because I like to have a little more contact when I'm not clipped in (yet). I'm currently riding the Candy 3 pedals although I have some cheaper Candy pedals on one of my bikes I think.

Your Knees May appreciate that float, rather than be forced into working with rigid, but wrong, angle. ..

I started on SPD's, and while they were acceptable, it was a real awakening when I bought Time ATACs. There is an experience that nearly every clipless user has, and that is the "fall-over while clipped in". SPD's, had a couple of those, but the only one with Times was when my buddy fell ON me. Yet I never accidentally unclipped, either. Times are great!

I'm on pinned flats right now, because poor shoes are as much a disqualifier as poor pedals. Replacements are not in the budget.

Like EB's/Candys, ATAC's (the older ones, anyway, I've heard that newer ATAC does have adjustment for tension) do not have a tension screw. Never missed it. Plus, my ATAC's had a SWEEEEET spot for engagement.

Very good info.

I just got a pair of Shimano MT34's shoes and a pair of MT780 pedals for Christmas, I was wondering how they might feel.

I have lots of bikes with SPD pedals and lots of shoes with SPD cleats, so clearly, I'm committed and like SPDs. With practice, I can locate the cleat on my shoes very quickly. Sometimes I plunk my foot down in just the right spot, and sometimes I get it close and can move it quickly and engage the cleat. Think about how finely tuned a violinist's finger location is. We can do amazing things with practice, and they eventually become easy.

Bingo... I guess I won't worry about it.

If you find in a week or 2 they are just not working for you upgrade. I bought a secondhand pair of time pedals and shoes to make the transition and though I liked the pedaling action the clipping in and out was a hassle. I invested $200 in SPD pedals and new shoes and couldn't believe the difference. Once when I stopped and forgot to clip out I panicked and in the process, clipped out before I fell over. The guy in the shop had set the release pressure very low thankfully.

I have since converted all my bikes to SPD and even have a new set spare as an ornament
The pedals are ridiculously cheep if you shop around.

They feel great, and you can walk around easily. I just got a pair and put 55 miles on a pair Jan 1