Taxonomy: Too many tags?
Nope, the taxonomy module can handle as many terms-per-vocab as your hardware will allow it to (within some reasonable theoretical bounds I'm sure, but certainly 140,000 terms would not be too much these days).

The 'problem' is in your server configuration. Quite simply you don't have enough available memory for the taxonomy module to process as many records as it needs to.

Try increasing the PHP memory_limit setting gradually and hopefully you'll be able to come to an acceptable compromise between your available memory and the size of your vocabularies.

Just to preempt what I think your response will be - you're already allocating 256MB, which might be a large (even outrageous) amount of maximum memory to give to a single PHP script, but the fact that you're getting out of memory errors means it's simply not enough for your site and needs to be increased (unless you want to optimise the core taxonomy module which I don't think would be much fun).

If you're on shared hosting, the first thing to do would be to get the site on a dedicated server/VM. That should make a good bit of difference.