You mentioned that this is for a scripted find. How is that detail part of what you describe here?
Do you have any script triggers on that field?
The pokiest find is in layouts with a couple dozen fields that represent a typical FileMaker find; that is, the script takes the user into find mode, goes to the appropriate layout, and then ends. They enter data into the fields, and then press a button to run another script which executes the find. Pretty normal, this part of things. And, there are no script triggers involved.
It's just that clicking into the fields, it takes a couple of seconds before text entry can occur. This does not conform with user expectations. It is compounded by the fact that the cursor moves immediately to the field, but text is not enterable right away. When the user sees the cursor blinking in the field, they assume they can start typing.
It is worth noting, perhaps, that even layouts with just one field (e.g. a pop-up menu) seem to take almost this long to become data-enterable. (Such routines have the user selecting the value in browse mode instead of find mode, and then the execution script is triggered on object modify.)
Other than this delay in field-enterability, the performance is okay.
To all who may wonder... after despairing of any other solution (like, someone knows why there might be a two second delay in field entry), I tried using a simpler theme, removing tooltips, placeholder text, stripping out certain fields... nothing worked.
Then, I tried methodically removing all elements, and much to my surprise, it was popovers that caused the delay. A single popover (there are several) present on the layout causes the delay. Conversely, leaving the layout in its original rococo glory (not that busy actually), with all the helpful and cool stuff, but removing the popovers (each of which had buttons to further the user in the program flow) eliminated the problem. As a final test, I left one popover, but removed the single button within it. Still... the delay... same as before.
My conclusion: popovers in WebDirect (at least on an iPhone) will cause a significant delay in the ability to enter data into a field, anywhere on the layout. Further, it doesn't only affect the first field you try to enter, but every single field.
I recommend that you post your findings in the Report an Issue section to bring this to the attention of the TS personnel that monitor that section of the forum.