Permanent teleportation circles are for creating "custom" teleport destinations, such as a party's home base. Permanent teleportation circles themselves are only destinations, as you said. They don't allow you to teleport from them without casting the Teleportation Circle spell.

Specific exploits

Simulacrum

With simulacrum, you have a perfectly loyal schmuck who can take all of those negatives for you. They can chill in their permanent Mordenkainen's magnificent mansion being waited on by 100 servants, while you run around with permanent invulnerability.

Wish

Wish can be used to cast spell permanency in 1 Action by duplicating its effects. This would allow you to make an unwilling target's spell permanent or to make a spell permanent on short notice. I cannot think of a specific exploit this would allow, but the behavior may be unintended. Wish will also waive the component cost, which should be minor anyways at the level you can cast wish.

This could be avoided by raising the level of spell permanency to 9th.

Amulet of Health and a warhorse

With some preparation, you can cast the spell yourself. The most debilitating of the three stresses is the reduction in your Constitution score. The rare magic item Amulet of Health sets your Constitution score to 19, which should override the reduction.

Now that you don't die from a stiff breeze, buy yourself a warhorse. You can cruise around at 120' per round as if nothing happened. Better yet, splurge on twelve warhorses - they tend to evaporate at the first sign of fireball.

Speaking of fireball...

Delayed blast fireball

Delayed blast fireball could theoretically deal infinite damage. It starts at 12d6 damage and increases by 1d6 every six seconds. After waiting one day, it will deal 14412d6 fire damage for an average of 50,442 fire damage on a failed save. I hope the target has Evasion or fire immunity!

If you can pick the field of battle, you turn said field - and anyone in it - into a smoking crater. If you can't, you'll need a way to move the bead to where you want. Delayed blast fireball provides the following option:

If the glowing bead is touched before the interval has expired, the creature touching it must make a Dexterity saving throw. On a failed save, the spell ends immediately, causing the bead to erupt in flame. On a successful save, the creature can throw the bead up to 40 feet. When it strikes a creature or a solid object, the spell ends, and the bead explodes.

As BlueHairedMeerkat points out in the comments, the spell doesn't say you can move the bead, only touch and then throw it. The spell says you can throw it, so I am unsure what happens if you choose to touch the bead, pass the save, and then not throw it. Would telekinesis work? What if you're teleported while holding the bead? Your DM may or may not allow you to carry your nuke around.

If your DM allows you to transport the bead, a character can start by making a Dexterity saving throw against the caster's spell save DC. A 17th level rogue can have a +11 to Dexterity saving throws, which rises to +16 standing next to a paladin with 20 Charisma. Throw in the resistance cantrip and a Ring of Protection and they can carry the bead completely safely.

Specific limitations

Concentration

You cannot cast spell permanency on a spell for which you are maintaining concentration. This is because any spell with a casting time longer than 1 Action requires concentration while you are casting it, which will end any other spell you are concentrating on. (Since the duration becomes "permanent", not "Concentration, permanent", I am assuming that any concentration requirement is lifted once spell permanency is completed.)

This limitation is lifted by using wish to duplicate spell permanency.

Balance

The current incarnation is very overpowered, especially for a 5th-level spell. Even as a 9th-level spell, its power would rival wish.

As Ben Barden says in his answer, this spell is nearly impossible to balance. Either you have enough restrictions that no one will use it, or you don't, and everyone will. As new source material comes out, you would need to evaluate each new spell for further exploits. It may instead be easier to create a series of magic items or long-to-infinite duration versions of existing spells, which could each be balanced separately.