Republican Gov. James A. Rhodes, considered a year ago by many political observers to be unbeatable, may be heading for a photo finish, against Lt. Gov. Richard F. Celeste, his Democratic challenger in the Nov. 7 election.

Recent statewide polls indicate the three-term governor, who will be 69 on Sept. 13, has lost his commanding lead over Celeste-an aggressive and articulate campaigner who has spent the past four years preparing for this year's race.

Although both sides have been sitting tightly on their respective polls, a statewide Republican poll by Robert Teeter reportedly showed Rhodes holding only a four-point lead over Celeste. Democrats say their polls indicate a still closer margin.

And the latest Columbus Dispatch poll - an unscientific voting machine survey that has somehow maintained a good track record over the years-revealed that Celeste has passed Rhodes for the first time, 49 percent to 47 percent.

In contrast, Democratic polls taken last fall showed Rhodes ahead by about 20 points.

All this has caused concern among the governor's supporters and high optimism in the Celeste camp.

Rhodes' top campaign aide, Kent McGough, continues to insist that Rhodes is in "good shape" and has shrugged off the Dispatch figures, saving, "It's not a poll."

But some key Republicans are plainly worried, and are saying so in their not-for-attribution conversations with reporters. They believe the governor is in trouble-though not necessarity fatal-because of his age and his long incumbency during which a number of state problems have worsened. Most notable among these are the intensifying public school financing ills around the state and the loss of jobs in industrial centers like Youngstown and Akron.

Except for a four-year break from 1970 to 1974, when he was forced to step down because the law prohibited three consecutive terms, Rhodes has been governor since 1963.

Celeste, a 40-year-old Phi Beta Kappa from Yale with a gregarious manner on the stump, has been hammering at the governor's record, insisting it is a series of "broken promises."

He has put together a field organization in all of the state's 88 counties, developed strong labor support and - unlike Rhodess' pass rivals - has dogged the governor in the latter's back yard: the county and state fair circuit, where the governor has long moved informally among the fairgoers as a folksy enthusiast of the annual summer gatherings.

Celeste also has brought in media specialist David Garth for the fall campaign to counter a high-priced media effort by Rhodes, who is again using John Deardourff, the adviser who helped Rhodes upset Democratic Gov. John J. Gilligan in 1974.

Rhodes reportedly will spend more than $1.2 million for media; Celeste, more than $500,000. And many political observers on both sides now believe the outcome may very well be decided in the voters' TV rooms by election day.